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%% This BibTeX bibliography file was created using BibDesk.
%% https://bibdesk.sourceforge.io/
%% Created for Giacomo Torlai at 2020-05-26 12:26:10 -0400
%% Saved with string encoding Unicode (UTF-8)
@misc{coderepo,
title={https://github.com/GTorlai/NeuralNetworks-for-Quantum},
url={https://github.com/GTorlai/NeuralNetworks-for-Quantum}
}
@ARTICLE{2012arXiv1212.5701Z,
author = {{Zeiler}, Matthew D.},
title = "{ADADELTA: An Adaptive Learning Rate Method}",
journal = {arXiv e-prints},
keywords = {Computer Science - Machine Learning},
year = 2012,
month = dec,
eid = {arXiv:1212.5701},
pages = {arXiv:1212.5701},
archivePrefix = {arXiv},
eprint = {1212.5701},
primaryClass = {cs.LG},
adsurl = {https://ui.adsabs.harvard.edu/abs/2012arXiv1212.5701Z},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2020arXiv201212281E,
author = {{Ebadi}, Sepehr and {Wang}, Tout T. and {Levine}, Harry and {Keesling}, Alexander and {Semeghini}, Giulia and {Omran}, Ahmed and {Bluvstein}, Dolev and {Samajdar}, Rhine and {Pichler}, Hannes and {Ho}, Wen Wei and {Choi}, Soonwon and {Sachdev}, Subir and {Greiner}, Markus and {Vuletic}, Vladan and {Lukin}, Mikhail D.},
title = "{Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Quantum Gases, Physics - Atomic Physics},
year = 2020,
month = dec,
eid = {arXiv:2012.12281},
pages = {arXiv:2012.12281},
archivePrefix = {arXiv},
eprint = {2012.12281},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201212281E},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2020arXiv201212268S,
author = {{Scholl}, Pascal and {Schuler}, Michael and {Williams}, Hannah J. and {Eberharter}, Alexander A. and {Barredo}, Daniel and {Schymik}, Kai-Niklas and {Lienhard}, Vincent and {Henry}, Louis-Paul and {Lang}, Thomas C. and {Lahaye}, Thierry and {L{\"a}uchli}, Andreas M. and {Browaeys}, Antoine},
title = "{Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Quantum Gases, Physics - Atomic Physics},
year = 2020,
month = dec,
eid = {arXiv:2012.12268},
pages = {arXiv:2012.12268},
archivePrefix = {arXiv},
eprint = {2012.12268},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201212268S},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{mnih_human-level_2015,
title = {Human-level control through deep reinforcement learning},
volume = {518},
issn = {1476-4687},
url = {https://doi.org/10.1038/nature14236},
doi = {10.1038/nature14236},
abstract = {An artificial agent is developed that learns to play a diverse range of classic Atari 2600 computer games directly from sensory experience, achieving a performance comparable to that of an expert human player; this work paves the way to building general-purpose learning algorithms that bridge the divide between perception and action.},
number = {7540},
journal = {Nature},
author = {Mnih, Volodymyr and Kavukcuoglu, Koray and Silver, David and Rusu, Andrei A. and Veness, Joel and Bellemare, Marc G. and Graves, Alex and Riedmiller, Martin and Fidjeland, Andreas K. and Ostrovski, Georg and Petersen, Stig and Beattie, Charles and Sadik, Amir and Antonoglou, Ioannis and King, Helen and Kumaran, Dharshan and Wierstra, Daan and Legg, Shane and Hassabis, Demis},
month = feb,
year = {2015},
pages = {529--533},
}
@book{becca_sorella_2017, place={Cambridge}, title={Quantum Monte Carlo Approaches for Correlated Systems}, DOI={10.1017/9781316417041}, publisher={Cambridge University Press}, author={Becca, Federico and Sorella, Sandro}, year={2017}}
@ARTICLE{2014arXiv1412.6980K,
author = {{Kingma}, Diederik P. and {Ba}, Jimmy},
title = "{Adam: A Method for Stochastic Optimization}",
journal = {arXiv e-prints},
keywords = {Computer Science - Machine Learning},
year = 2014,
month = dec,
eid = {arXiv:1412.6980},
pages = {arXiv:1412.6980},
archivePrefix = {arXiv},
eprint = {1412.6980},
primaryClass = {cs.LG},
adsurl = {https://ui.adsabs.harvard.edu/abs/2014arXiv1412.6980K},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{haffner_scalable_2005,
title = {Scalable multiparticle entanglement of trapped ions},
volume = {438},
issn = {1476-4687},
url = {https://doi.org/10.1038/nature04279},
doi = {10.1038/nature04279},
abstract = {Schrödinger's hypothetical cat was both dead and alive thanks to a paradox of quantum mechanics, in which a system exists in two or more states at once in a ‘superposition’ of entangled states. Creating this situation experimentally is very difficult, especially for systems made up of many particles, as interactions with the environment destroy superposition in a process called decoherence. So far, entangled states of just a handful of atoms or photons have been achieved. Now, two groups have extended the limits of quantum state engineering by creating the largest entangled atomic systems to date. Working with atoms held in an ion trap by an electromagnetic field to limit decoherence, a team from the National Institute of Standards and Technology in Boulder, Colorado, has created ‘cat states’ of up to six beryllium atoms. A second group, based at Innsbruck University in Austria, has achieved a similar feat by making a related entangled state, a ‘W state’, containing up to eight particles. As the states are created ‘on demand’ and should be scalable to many more particles, there is hope that this technology will pave the way for building a large-scale quantum computer.},
number = {7068},
journal = {Nature},
author = {Häffner, H. and Hänsel, W. and Roos, C. F. and Benhelm, J. and Chek-al-kar, D. and Chwalla, M. and Körber, T. and Rapol, U. D. and Riebe, M. and Schmidt, P. O. and Becher, C. and Gühne, O. and Dür, W. and Blatt, R.},
month = dec,
year = {2005},
pages = {643--646},
}
@ARTICLE{Bravyi2006,
author = {{Bravyi}, Sergey and {DiVincenzo}, David P. and {Oliveira}, Roberto I. and {Terhal}, Barbara M.},
title = "{The Complexity of Stoquastic Local Hamiltonian Problems}",
journal = {arXiv e-prints},
keywords = {Quantum Physics},
year = 2006,
month = jun,
eid = {quant-ph/0606140},
pages = {quant-ph/0606140},
archivePrefix = {arXiv},
eprint = {quant-ph/0606140},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2006quant.ph..6140B},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{LeRoux2008,
author = {Le Roux, Nicolas and Bengio, Yoshua},
title = {Representational Power of Restricted Boltzmann Machines and Deep Belief Networks},
journal = {Neural Computation},
volume = {20},
number = {6},
pages = {1631-1649},
year = {2008},
doi = {10.1162/neco.2008.04-07-510},
URL = {
https://doi.org/10.1162/neco.2008.04-07-510
},
eprint = {
https://doi.org/10.1162/neco.2008.04-07-510
}
,
abstract = { Deep belief networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton, Osindero, and Teh (2006) along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a restricted Boltzmann machine (RBM), used to represent one layer of the model. Restricted Boltzmann machines are interesting because inference is easy in them and because they have been successfully used as building blocks for training deeper models. We first prove that adding hidden units yields strictly improved modeling power, while a second theorem shows that RBMs are universal approximators of discrete distributions. We then study the question of whether DBNs with more layers are strictly more powerful in terms of representational power. This suggests a new and less greedy criterion for training RBMs within DBNs. }
}
@article{PhysRevLett.120.190501,
title = {Fidelity Witnesses for Fermionic Quantum Simulations},
author = {Gluza, M. and Kliesch, M. and Eisert, J. and Aolita, L.},
journal = {Phys. Rev. Lett.},
volume = {120},
issue = {19},
pages = {190501},
numpages = {7},
year = {2018},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.120.190501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.190501}
}
@article{aolita_reliable_2015,
title = {Reliable quantum certification of photonic state preparations},
volume = {6},
issn = {2041-1723},
url = {https://doi.org/10.1038/ncomms9498},
doi = {10.1038/ncomms9498},
abstract = {Quantum technologies promise a variety of exciting applications. Even though impressive progress has been achieved recently, a major bottleneck currently is the lack of practical certification techniques. The challenge consists of ensuring that classically intractable quantum devices perform as expected. Here we present an experimentally friendly and reliable certification tool for photonic quantum technologies: an efficient certification test for experimental preparations of multimode pure Gaussian states, pure non-Gaussian states generated by linear-optical circuits with Fock-basis states of constant boson number as inputs, and pure states generated from the latter class by post-selecting with Fock-basis measurements on ancillary modes. Only classical computing capabilities and homodyne or hetorodyne detection are required. Minimal assumptions are made on the noise or experimental capabilities of the preparation. The method constitutes a step forward in many-body quantum certification, which is ultimately about testing quantum mechanics at large scales.},
number = {1},
journal = {Nature Communications},
author = {Aolita, Leandro and Gogolin, Christian and Kliesch, Martin and Eisert, Jens},
month = nov,
year = {2015},
pages = {8498},
}
@article{PhysRevLett.106.230501,
title = {Direct Fidelity Estimation from Few Pauli Measurements},
author = {Flammia, Steven T. and Liu, Yi-Kai},
journal = {Phys. Rev. Lett.},
volume = {106},
issue = {23},
pages = {230501},
numpages = {4},
year = {2011},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.106.230501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.106.230501}
}
@article{PhysRevA.99.052350,
title = {Statistical analysis of randomized benchmarking},
author = {Harper, Robin and Hincks, Ian and Ferrie, Chris and Flammia, Steven T. and Wallman, Joel J.},
journal = {Phys. Rev. A},
volume = {99},
issue = {5},
pages = {052350},
numpages = {7},
year = {2019},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.99.052350},
url = {https://link.aps.org/doi/10.1103/PhysRevA.99.052350}
}
@article{PhysRevA.85.042311,
title = {Characterizing quantum gates via randomized benchmarking},
author = {Magesan, Easwar and Gambetta, Jay M. and Emerson, Joseph},
journal = {Phys. Rev. A},
volume = {85},
issue = {4},
pages = {042311},
numpages = {16},
year = {2012},
month = {Apr},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.85.042311},
url = {https://link.aps.org/doi/10.1103/PhysRevA.85.042311}
}
@article{PhysRevA.77.012307,
title = {Randomized benchmarking of quantum gates},
author = {Knill, E. and Leibfried, D. and Reichle, R. and Britton, J. and Blakestad, R. B. and Jost, J. D. and Langer, C. and Ozeri, R. and Seidelin, S. and Wineland, D. J.},
journal = {Phys. Rev. A},
volume = {77},
issue = {1},
pages = {012307},
numpages = {7},
year = {2008},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.77.012307},
url = {https://link.aps.org/doi/10.1103/PhysRevA.77.012307}
}
@article{PhysRevLett.105.250403,
title = {Permutationally Invariant Quantum Tomography},
author = {T\'oth, G. and Wieczorek, W. and Gross, D. and Krischek, R. and Schwemmer, C. and Weinfurter, H.},
journal = {Phys. Rev. Lett.},
volume = {105},
issue = {25},
pages = {250403},
numpages = {4},
year = {2010},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.105.250403},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.105.250403}
}
@article{Moroder_2012,
doi = {10.1088/1367-2630/14/10/105001},
url = {https://doi.org/10.1088%2F1367-2630%2F14%2F10%2F105001},
year = 2012,
month = {oct},
publisher = {{IOP} Publishing},
volume = {14},
number = {10},
pages = {105001},
author = {Tobias Moroder and Philipp Hyllus and G{\'{e}}za T{\'{o}}th and Christian Schwemmer and Alexander Niggebaum and Stefanie Gaile and Otfried Gühne and Harald Weinfurter},
title = {Permutationally invariant state reconstruction},
journal = {New Journal of Physics},
abstract = {Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography. It works for all common state-of-the-art reconstruction principles, including, in particular, maximum likelihood and least squares methods, which are the preferred choices in today's experiments. This high efficiency is achieved by greatly reducing the dimensionality of the problem employing a particular representation of permutationally invariant states known from spin coupling combined with convex optimization, which has clear advantages regarding speed, control and accuracy in comparison to commonly employed numerical routines. First prototype implementations easily allow reconstruction of a state of 20 qubits in a few minutes on a standard computer.}
}
@article{doi:10.1146/annurev-conmatphys-031218-013401,
author = {Knolle, J. and Moessner, R.},
title = {A Field Guide to Spin Liquids},
journal = {Annual Review of Condensed Matter Physics},
volume = {10},
number = {1},
pages = {451-472},
year = {2019},
doi = {10.1146/annurev-conmatphys-031218-013401},
URL = {
https://doi.org/10.1146/annurev-conmatphys-031218-013401
},
eprint = {
https://doi.org/10.1146/annurev-conmatphys-031218-013401
}
,
abstract = { Spin liquids are collective phases of quantum matter that have eluded discovery in correlated magnetic materials for over half a century. Theoretical models of these enigmatic topological phases are no longer in short supply. In experiment there also exist plenty of promising candidate materials for their realization. One of the central challenges for the clear diagnosis of a spin liquid has been to connect the two. From that perspective, this review discusses characteristic features in experiment, resulting from the unusual properties of spin liquids. This takes us to thermodynamic, spectroscopic, transport, and other experiments on a search for traces of emergent gauge fields, spinons, Majorana fermions, and other fractionalized particles. }
}
@article{savaryQuantumSpinLiquids2016,
title = {Quantum Spin Liquids: A Review},
shorttitle = {Quantum Spin Liquids},
author = {Savary, Lucile and Balents, Leon},
year = {2016},
month = nov,
volume = {80},
pages = {016502},
issn = {0034-4885},
doi = {10.1088/0034-4885/80/1/016502},
abstract = {Quantum spin liquids may be considered `quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.},
file = {/Users/carrasqu/Zotero/storage/3BN7MBES/Savary and Balents - 2016 - Quantum spin liquids a review.pdf},
journal = {Reports on Progress in Physics},
number = {1}
}
@article{RevModPhys.91.021001,
title = {Colloquium: Many-body localization, thermalization, and entanglement},
author = {Abanin, Dmitry A. and Altman, Ehud and Bloch, Immanuel and Serbyn, Maksym},
journal = {Rev. Mod. Phys.},
volume = {91},
issue = {2},
pages = {021001},
numpages = {26},
year = {2019},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/RevModPhys.91.021001},
url = {https://link.aps.org/doi/10.1103/RevModPhys.91.021001}
}
@article{basko2006,
title = {Metal\textendash Insulator Transition in a Weakly Interacting Many-Electron System with Localized Single-Particle States},
author = {Basko, D. M. and Aleiner, I. L. and Altshuler, B. L.},
year = {2006},
month = may,
volume = {321},
pages = {1126--1205},
issn = {0003-4916},
doi = {10.1016/j.aop.2005.11.014},
abstract = {We consider low-temperature behavior of weakly interacting electrons in disordered conductors in the regime when all single-particle eigenstates are localized by the quenched disorder. We prove that in the absence of coupling of the electrons to any external bath dc electrical conductivity exactly vanishes as long as the temperature T does not exceed some finite value Tc. At the same time, it can be also proven that at high enough T the conductivity is finite. These two statements imply that the system undergoes a finite temperature metal-to-insulator transition, which can be viewed as Anderson-like localization of many-body wave functions in the Fock space. Metallic and insulating states are not different from each other by any spatial or discrete symmetries. We formulate the effective Hamiltonian description of the system at low energies (of the order of the level spacing in the single-particle localization volume). In the metallic phase quantum Boltzmann equation is valid, allowing to find the kinetic coefficients. In the insulating phase, T},
file = {/Users/carrasqu/Zotero/storage/GUKFC79I/Basko et al. - 2006 - Metal–insulator transition in a weakly interacting.pdf},
journal = {Annals of Physics},
keywords = {Anderson localization,Fock space,Metal–insulator transition},
number = {5}
}
@book{Goodfellow-et-al-2016,
title={Deep Learning},
author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
publisher={MIT Press},
note={\url{http://www.deeplearningbook.org}},
year={2016}
}
@book{Xiao:803748,
author = "Wen Xiao Gang",
title = "{Quantum field theory of many-body systems: from the
origin of sound to an origin of light and electrons}",
publisher = "Oxford University Press",
address = "Oxford",
year = "2007",
url = "https://cds.cern.ch/record/803748",
doi = "10.1093/acprof:oso/9780199227259.001.0001",
}
@article{inack2018,
title = {Projective quantum Monte Carlo simulations guided by unrestricted neural network states},
author = {Inack, E. M. and Santoro, G. E. and Dell'Anna, L. and Pilati, S.},
journal = {Phys. Rev. B},
volume = {98},
issue = {23},
pages = {235145},
numpages = {9},
year = {2018},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.98.235145},
url = {https://link.aps.org/doi/10.1103/PhysRevB.98.235145}
}
@article{huang2017,
title = {Accelerated Monte Carlo simulations with restricted Boltzmann machines},
author = {Huang, Li and Wang, Lei},
journal = {Phys. Rev. B},
volume = {95},
issue = {3},
pages = {035105},
numpages = {6},
year = {2017},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.95.035105},
url = {https://link.aps.org/doi/10.1103/PhysRevB.95.035105}
}
@article{mcnaughton2020,
title = {Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks},
author = {McNaughton, B. and Milo\ifmmode \check{s}\else \v{s}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{}, M. V. and Perali, A. and Pilati, S.},
journal = {Phys. Rev. E},
volume = {101},
issue = {5},
pages = {053312},
numpages = {12},
year = {2020},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.101.053312},
url = {https://link.aps.org/doi/10.1103/PhysRevE.101.053312}
}
@article{xiao_yan2017,
title = {Self-learning quantum Monte Carlo method in interacting fermion systems},
author = {Xu, Xiao Yan and Qi, Yang and Liu, Junwei and Fu, Liang and Meng, Zi Yang},
journal = {Phys. Rev. B},
volume = {96},
issue = {4},
pages = {041119},
numpages = {5},
year = {2017},
month = {Jul},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.96.041119},
url = {https://link.aps.org/doi/10.1103/PhysRevB.96.041119}
}
@article{junwei2017,
title = {Self-learning Monte Carlo method},
author = {Liu, Junwei and Qi, Yang and Meng, Zi Yang and Fu, Liang},
journal = {Phys. Rev. B},
volume = {95},
issue = {4},
pages = {041101},
numpages = {5},
year = {2017},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.95.041101},
url = {https://link.aps.org/doi/10.1103/PhysRevB.95.041101}
}
@article{parolini2019,
title = {Tunneling in projective quantum Monte Carlo simulations with guiding wave functions},
author = {Parolini, T. and Inack, E. M. and Giudici, G. and Pilati, S.},
journal = {Phys. Rev. B},
volume = {100},
issue = {21},
pages = {214303},
numpages = {10},
year = {2019},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.100.214303},
url = {https://link.aps.org/doi/10.1103/PhysRevB.100.214303}
}
@article{Wu_2019,
title = {Solving Statistical Mechanics Using Variational Autoregressive Networks},
author = {Wu, Dian and Wang, Lei and Zhang, Pan},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {8},
pages = {080602},
numpages = {6},
year = {2019},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.080602},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.080602}
}
@article{albergo2019,
title = {Flow-based generative models for Markov chain Monte Carlo in lattice field theory},
author = {Albergo, M. S. and Kanwar, G. and Shanahan, P. E.},
journal = {Phys. Rev. D},
volume = {100},
issue = {3},
pages = {034515},
numpages = {13},
year = {2019},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevD.100.034515},
url = {https://link.aps.org/doi/10.1103/PhysRevD.100.034515}
}
@article{pilati2019,
title = {Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines},
author = {Pilati, S. and Inack, E. M. and Pieri, P.},
journal = {Phys. Rev. E},
volume = {100},
issue = {4},
pages = {043301},
numpages = {12},
year = {2019},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.100.043301},
url = {https://link.aps.org/doi/10.1103/PhysRevE.100.043301}
}
@article{PhysRevLett.122.250502,
title = {Neural-Network Approach to Dissipative Quantum Many-Body Dynamics},
author = {Hartmann, Michael J. and Carleo, Giuseppe},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {25},
pages = {250502},
numpages = {6},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.250502},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.250502}
}
@article{hermann2019deep,
title = {Deep-neural-network solution of the electronic {Schrödinger} equation},
volume = {12},
issn = {1755-4349},
url = {https://doi.org/10.1038/s41557-020-0544-y},
doi = {10.1038/s41557-020-0544-y},
abstract = {The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree–Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H10, and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient.},
number = {10},
journal = {Nature Chemistry},
author = {Hermann, Jan and Schätzle, Zeno and Noé, Frank},
month = oct,
year = {2020},
pages = {891--897},
}
@article{zi2018,
title = {Approximating quantum many-body wave functions using artificial neural networks},
author = {Cai, Zi and Liu, Jinguo},
journal = {Phys. Rev. B},
volume = {97},
issue = {3},
pages = {035116},
numpages = {8},
year = {2018},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.97.035116},
url = {https://link.aps.org/doi/10.1103/PhysRevB.97.035116}
}
@article{AD_2017,
author = {Baydin, Atilim Gunes and Pearlmutter, Barak A. and Radul, Alexey Andreyevich and Siskind, Jeffrey Mark},
title = {Automatic Differentiation in Machine Learning: A Survey},
year = {2017},
issue_date = {January 2017},
volume = {18},
number = {1},
issn = {1532-4435},
journal = {J. Mach. Learn. Res.}
}
@article{Zhang_MLcuprates,
Abstract = {For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena1. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science2--5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)6--16, the next challenge is to apply this approach to experimental data---for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Strong-coupling theories of electronic liquid crystals18,19 are consistent with these observations.},
Author = {Zhang, Yi and Mesaros, A. and Fujita, K. and Edkins, S. D. and Hamidian, M. H. and Ch'ng, K. and Eisaki, H. and Uchida, S. and Davis, J. C. S{\'e}amus and Khatami, Ehsan and Kim, Eun-Ah},
Da = {2019/06/01},
Date-Added = {2019-07-31 14:52:47 +0000},
Date-Modified = {2019-07-31 14:52:47 +0000},
Doi = {10.1038/s41586-019-1319-8},
Id = {Zhang2019},
Isbn = {1476-4687},
Journal = {Nature},
Number = {7762},
Pages = {484--490},
Title = {Machine learning in electronic-quantum-matter imaging experiments},
Ty = {JOUR},
Url = {https://doi.org/10.1038/s41586-019-1319-8},
Volume = {570},
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1038/s41586-019-1319-8}}
@article{leiwang2016,
title = {Discovering phase transitions with unsupervised learning},
author = {Wang, Lei},
journal = {Phys. Rev. B},
volume = {94},
issue = {19},
pages = {195105},
numpages = {5},
year = {2016},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.94.195105},
url = {https://link.aps.org/doi/10.1103/PhysRevB.94.195105}
}
@article{Bohrdt2018,
abstract = {Quantum gas microscopes for ultracold atoms can provide high-resolution real-space snapshots of complex many-body systems. We implement machine learning to analyze and classify such snapshots of ultracold atoms. Specifically, we compare the data from an experimental realization of the two-dimensional Fermi-Hubbard model to two theoretical approaches: a doped quantum spin liquid state of resonating valence bond type, and the geometric string theory, describing a state with hidden spin order. This approach considers all available information without a potential bias towards one particular theory by the choice of an observable and can therefore select the theory which is more predictive in general. Up to intermediate doping values, our algorithm tends to classify experimental snapshots as geometric-string-like, as compared to the doped spin liquid. Our results demonstrate the potential for machine learning in processing the wealth of data obtained through quantum gas microscopy for new physical insights.},
archivePrefix = {arXiv},
arxivId = {1811.12425},
author = {Bohrdt, Annabelle and Chiu, Christie S. and Ji, Geoffrey and Xu, Muqing and Greif, Daniel and Greiner, Markus and Demler, Eugene and Grusdt, Fabian and Knap, Michael},
eprint = {1811.12425},
file = {:Users/btimar/Library/Application Support/Mendeley Desktop/Downloaded/Bohrdt et al. - 2018 - Classifying Snapshots of the Doped Hubbard Model with Machine Learning.pdf:pdf},
month = {nov},
title = {{Classifying Snapshots of the Doped Hubbard Model with Machine Learning}},
url = {http://arxiv.org/abs/1811.12425},
year = {2018}
}
@article{Rem2018,
abstract = {Machine learning techniques such as artificial neural networks are currently revolutionizing many technological areas and have also proven successful in quantum physics applications. Here we employ an artificial neural network and deep learning techniques to identify quantum phase transitions from single-shot experimental momentum-space density images of ultracold quantum gases and obtain results, which were not feasible with conventional methods. We map out the complete two-dimensional topological phase diagram of the Haldane model and provide an accurate characterization of the superfluid-to-Mott-insulator transition in an inhomogeneous Bose-Hubbard system. Our work points the way to unravel complex phase diagrams of general experimental systems, where the Hamiltonian and the order parameters might not be known.},
archivePrefix = {arXiv},
arxivId = {1809.05519},
author = {Rem, Benno S. and K{\"{a}}ming, Niklas and Tarnowski, Matthias and Asteria, Luca and Fl{\"{a}}schner, Nick and Becker, Christoph and Sengstock, Klaus and Weitenberg, Christof},
eprint = {1809.05519},
file = {:Users/btimar/Library/Application Support/Mendeley Desktop/Downloaded/Rem et al. - 2018 - Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data.pdf:pdf},
month = {sep},
title = {{Identifying Quantum Phase Transitions using Artificial Neural Networks on Experimental Data}},
url = {http://arxiv.org/abs/1809.05519},
year = {2018}
}
@article{evert2017nature,
Author = {van Nieuwenburg, Evert P. L. and Liu, Ye-Hua and Huber, Sebastian D.},
Date = {2017/02/13/online},
Date-Added = {2019-07-31 14:55:45 +0000},
Date-Modified = {2019-07-31 14:55:45 +0000},
Day = {13},
Journal = {Nature Physics},
L3 = {10.1038/nphys4037; },
Month = {02},
Pages = {435},
Publisher = {Nature Publishing Group SN -},
Title = {Learning phase transitions by confusion},
Ty = {JOUR},
Url = {https://doi.org/10.1038/nphys4037},
Volume = {13},
Year = {2017},
Bdsk-Url-1 = {https://doi.org/10.1038/nphys4037}}
@ARTICLE{2020arXiv200905580L,
author = {{Luo}, Di and {Chen}, Zhuo and {Carrasquilla}, Juan and {Clark}, Bryan K.},
title = "{Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation}",
journal = {arXiv e-prints},
keywords = {Condensed Matter - Strongly Correlated Electrons, Condensed Matter - Disordered Systems and Neural Networks, Physics - Computational Physics, Quantum Physics},
year = 2020,
month = sep,
eid = {arXiv:2009.05580},
pages = {arXiv:2009.05580},
archivePrefix = {arXiv},
eprint = {2009.05580},
primaryClass = {cond-mat.str-el},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200905580L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2019arXiv191211052C,
author = {{Carrasquilla}, Juan and {Luo}, Di and {P{\'e}rez}, Felipe and {Milsted}, Ashley and {Clark}, Bryan K. and {Volkovs}, Maksims and {Aolita}, Leandro},
title = "{Probabilistic Simulation of Quantum Circuits with the Transformer}",
journal = {arXiv e-prints},
keywords = {Condensed Matter - Strongly Correlated Electrons, Condensed Matter - Disordered Systems and Neural Networks, Quantum Physics},
year = 2019,
month = dec,
eid = {arXiv:1912.11052},
pages = {arXiv:1912.11052},
archivePrefix = {arXiv},
eprint = {1912.11052},
primaryClass = {cond-mat.str-el},
adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv191211052C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{kandala_hardware-efficient_2017,
title = {Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets},
volume = {549},
issn = {1476-4687},
url = {https://doi.org/10.1038/nature23879},
doi = {10.1038/nature23879},
abstract = {The ground-state energy of small molecules is determined efficiently using six qubits of a superconducting quantum processor.},
number = {7671},
journal = {Nature},
author = {Kandala, Abhinav and Mezzacapo, Antonio and Temme, Kristan and Takita, Maika and Brink, Markus and Chow, Jerry M. and Gambetta, Jay M.},
month = sep,
year = {2017},
pages = {242--246},
}
@article{choo_fermionicnqs2020,
title = {Fermionic neural-network states for ab-initio electronic structure},
volume = {11},
issn = {2041-1723},
url = {https://doi.org/10.1038/s41467-020-15724-9},
doi = {10.1038/s41467-020-15724-9},
abstract = {Neural-network quantum states have been successfully used to study a variety of lattice and continuous-space problems. Despite a great deal of general methodological developments, representing fermionic matter is however still early research activity. Here we present an extension of neural-network quantum states to model interacting fermionic problems. Borrowing techniques from quantum simulation, we directly map fermionic degrees of freedom to spin ones, and then use neural-network quantum states to perform electronic structure calculations. For several diatomic molecules in a minimal basis set, we benchmark our approach against widely used coupled cluster methods, as well as many-body variational states. On some test molecules, we systematically improve upon coupled cluster methods and Jastrow wave functions, reaching chemical accuracy or better. Finally, we discuss routes for future developments and improvements of the methods presented.},
number = {1},
journal = {Nature Communications},
author = {Choo, Kenny and Mezzacapo, Antonio and Carleo, Giuseppe},
month = may,
year = {2020},
pages = {2368},
}
@article{carrasquilla2017nature,
Author = {Carrasquilla, Juan and Melko, Roger G.},
Date = {2017/02/13/online},
Date-Added = {2019-07-31 14:55:21 +0000},
Date-Modified = {2019-07-31 14:55:21 +0000},
Day = {13},
Journal = {Nature Physics},
L3 = {10.1038/nphys4035; https://www.nature.com/articles/nphys4035#supplementary-information},
Month = {02},
Pages = {431},
Publisher = {Nature Publishing Group SN -},
Title = {Machine learning phases of matter},
Ty = {JOUR},
Url = {https://doi.org/10.1038/nphys4035},
Volume = {13},
Year = {2017},
Bdsk-Url-1 = {https://doi.org/10.1038/nphys4035}}
@article{androsiuk1993,
title = "Neural network solution of the Schroedinger equation for a two-dimensional harmonic oscillator",
journal = "Chemical Physics",
volume = "173",
number = "3",
pages = "377 - 383",
year = "1993",
issn = "0301-0104",
doi = "https://doi.org/10.1016/0301-0104(93)80153-Z",
url = "http://www.sciencedirect.com/science/article/pii/030101049380153Z",
author = "J. Androsiuk and L. Kulak and K. Sienicki",
}
@ARTICLE{LAGARIS19971,
author={I. E. {Lagaris} and A. {Likas} and D. I. {Fotiadis}},
journal={IEEE Transactions on Neural Networks},
title={Artificial neural networks for solving ordinary and partial differential equations},
year={1998},
volume={9},
number={5},
pages={987-1000},
doi={10.1109/72.712178}}
@article {Carleo_2017,
author = {Carleo, Giuseppe and Troyer, Matthias},
title = {Solving the quantum many-body problem with artificial neural networks},
volume = {355},
number = {6325},
pages = {602--606},
year = {2017},
doi = {10.1126/science.aag2302},
publisher = {American Association for the Advancement of Science},
abstract = {Elucidating the behavior of quantum interacting systems of many particles remains one of the biggest challenges in physics. Traditional numerical methods often work well, but some of the most interesting problems leave them stumped. Carleo and Troyer harnessed the power of machine learning to develop a variational approach to the quantum many-body problem (see the Perspective by Hush). The method performed at least as well as state-of-the-art approaches, setting a benchmark for a prototypical two-dimensional problem. With further development, it may well prove a valuable piece in the quantum toolbox.Science, this issue p. 602; see also p. 580The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.},
issn = {0036-8075},
journal = {Science}
}
@article{PhysRevLett.122.250501,
title = {Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems},
author = {Nagy, Alexandra and Savona, Vincenzo},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {25},
pages = {250501},
numpages = {6},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.250501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.250501}
}
@article{Di_Luo,
title = {Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions},
author = {Luo, Di and Clark, Bryan K.},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {22},
pages = {226401},
numpages = {6},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.226401},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.226401}
}
@article{pfau2019abinitio,
title = {Ab initio solution of the many-electron Schr\"odinger equation with deep neural networks},
author = {Pfau, David and Spencer, James S. and Matthews, Alexander G. D. G. and Foulkes, W. M. C.},
journal = {Phys. Rev. Research},
volume = {2},
issue = {3},
pages = {033429},
numpages = {20},
year = {2020},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.033429},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.033429}
}
@ARTICLE{roth2020iterative,
author = {{Roth}, Christopher},
title = "{Iterative Retraining of Quantum Spin Models Using Recurrent Neural Networks}",
journal = {arXiv e-prints},
keywords = {Physics - Computational Physics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Strongly Correlated Electrons},
year = 2020,
month = mar,
eid = {arXiv:2003.06228},
pages = {arXiv:2003.06228},
archivePrefix = {arXiv},
eprint = {2003.06228},
primaryClass = {physics.comp-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200306228R},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{RNNWF_2020,
title = {Recurrent neural network wave functions},
author = {Hibat-Allah, Mohamed and Ganahl, Martin and Hayward, Lauren E. and Melko, Roger G. and Carrasquilla, Juan},
journal = {Phys. Rev. Research},
volume = {2},
issue = {2},
pages = {023358},
numpages = {17},
year = {2020},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.023358},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023358}
}
@article{PhysRevLett.124.020503,
title = {Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems},
author = {Sharir, Or and Levine, Yoav and Wies, Noam and Carleo, Giuseppe and Shashua, Amnon},
journal = {Phys. Rev. Lett.},
volume = {124},
issue = {2},
pages = {020503},
numpages = {6},
year = {2020},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.124.020503},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.020503}
}
@article{PhysRevLett.122.250503,
title = {Variational Neural-Network Ansatz for Steady States in Open Quantum Systems},
author = {Vicentini, Filippo and Biella, Alberto and Regnault, Nicolas and Ciuti, Cristiano},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {25},
pages = {250503},
numpages = {6},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.250503},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.250503}
}
@article{PhysRevB.99.214306,
title = {Constructing neural stationary states for open quantum many-body systems},
author = {Yoshioka, Nobuyuki and Hamazaki, Ryusuke},
journal = {Phys. Rev. B},
volume = {99},
issue = {21},
pages = {214306},
numpages = {8},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.99.214306},
url = {https://link.aps.org/doi/10.1103/PhysRevB.99.214306}
}
@ARTICLE{2020arXiv201014510L,
author = {{Lode}, Axel U.~J. and {Lin}, Rui and {B{\"u}ttner}, Miriam and {Papariello}, Luca and {L{\'e}v{\^e}que}, Camille and {Chitra}, R. and {Tsatsos}, Marios C. and {Jaksch}, Dieter and {Molignini}, Paolo},
title = "{Optimized Observable Readout from Single-shot Images of Ultracold Atoms via Machine Learning}",
journal = {arXiv e-prints},
keywords = {Condensed Matter - Quantum Gases, Quantum Physics},
year = 2020,
month = oct,
eid = {arXiv:2010.14510},
pages = {arXiv:2010.14510},
archivePrefix = {arXiv},
eprint = {2010.14510},
primaryClass = {cond-mat.quant-gas},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201014510L},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevLett.122.210503,
title = {Machine Learning Topological Phases with a Solid-State Quantum Simulator},
author = {Lian, Wenqian and Wang, Sheng-Tao and Lu, Sirui and Huang, Yuanyuan and Wang, Fei and Yuan, Xinxing and Zhang, Wengang and Ouyang, Xiaolong and Wang, Xin and Huang, Xianzhi and He, Li and Chang, Xiuying and Deng, Dong-Ling and Duan, Luming},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {21},
pages = {210503},
numpages = {5},
year = {2019},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.210503},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.210503}
}
@article{PhysRevB.99.121104,
title = {Machine learning of quantum phase transitions},
author = {Dong, Xiao-Yu and Pollmann, Frank and Zhang, Xue-Feng},
journal = {Phys. Rev. B},
volume = {99},
issue = {12},
pages = {121104},
numpages = {6},
year = {2019},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.99.121104},
url = {https://link.aps.org/doi/10.1103/PhysRevB.99.121104}
}
@article{berezutskii2020,
title = {Probing Criticality in Quantum Spin Chains with Neural Networks},
author = {Berezutskii, A. and Beketov, M. and Yudin, D. and Zimbor{\'a}s, Z. and Biamonte, J. D.},
year = {2020},
month = aug,
volume = {1},
pages = {03LT01},
publisher = {{IOP Publishing}},
issn = {2632-072X},
doi = {10.1088/2632-072X/abaa2b},
abstract = {The numerical emulation of quantum systems often requires an exponential number of degrees of freedom which translates to a computational bottleneck. Methods of machine learning have been used in adjacent fields for effective feature extraction and dimensionality reduction of high-dimensional datasets. Recent studies have revealed that neural networks are further suitable for the determination of macroscopic phases of matter and associated phase transitions as well as efficient quantum state representation. In this work, we address quantum phase transitions in quantum spin chains, namely the transverse field Ising chain and the anisotropic XY chain, and show that even neural networks with no hidden layers can be effectively trained to distinguish between magnetically ordered and disordered phases. Our neural network acts to predict the corresponding crossovers finite-size systems undergo. Our results extend to a wide class of interacting quantum many-body systems and illustrate the wide applicability of neural networks to many-body quantum physics.},
journal = {Journal of Physics: Complexity},
number = {3}
}
@article{PhysRevLett.125.170603,
title = {Unsupervised Phase Discovery with Deep Anomaly Detection},
author = {Kottmann, Korbinian and Huembeli, Patrick and Lewenstein, Maciej and Ac\'{\i}n, Antonio},
journal = {Phys. Rev. Lett.},
volume = {125},
issue = {17},
pages = {170603},
numpages = {6},
year = {2020},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.125.170603},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.170603}
}
@article{PhysRevB.102.054512,
title = {Deep learning of topological phase transitions from entanglement aspects},
author = {Tsai, Yuan-Hong and Yu, Meng-Zhe and Hsu, Yu-Hao and Chung, Ming-Chiang},
journal = {Phys. Rev. B},
volume = {102},
issue = {5},
pages = {054512},
numpages = {8},
year = {2020},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.102.054512},
url = {https://link.aps.org/doi/10.1103/PhysRevB.102.054512}
}
@article{PhysRevB.99.060404,
title = {Probing hidden spin order with interpretable machine learning},
author = {Greitemann, Jonas and Liu, Ke and Pollet, Lode},
journal = {Phys. Rev. B},
volume = {99},
issue = {6},
pages = {060404},
numpages = {6},
year = {2019},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.99.060404},
url = {https://link.aps.org/doi/10.1103/PhysRevB.99.060404}
}
@article{PhysRevB.99.104410,
title = {Learning multiple order parameters with interpretable machines},
author = {Liu, Ke and Greitemann, Jonas and Pollet, Lode},
journal = {Phys. Rev. B},
volume = {99},
issue = {10},
pages = {104410},
numpages = {15},
year = {2019},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.99.104410},
url = {https://link.aps.org/doi/10.1103/PhysRevB.99.104410}
}
@article{PhysRevLett.124.010508,
title = {Discovering Physical Concepts with Neural Networks},
author = {Iten, Raban and Metger, Tony and Wilming, Henrik and del Rio, L\'{\i}dia and Renner, Renato},
journal = {Phys. Rev. Lett.},
volume = {124},
issue = {1},
pages = {010508},
numpages = {6},
year = {2020},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.124.010508},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.010508}
}
@article{PhysRevX.10.011006,
title = {Using a Recurrent Neural Network to Reconstruct Quantum Dynamics of a Superconducting Qubit from Physical Observations},
author = {Flurin, E. and Martin, L. S. and Hacohen-Gourgy, S. and Siddiqi, I.},
journal = {Phys. Rev. X},
volume = {10},
issue = {1},
pages = {011006},
numpages = {10},
year = {2020},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevX.10.011006},
url = {https://link.aps.org/doi/10.1103/PhysRevX.10.011006}
}
@article{PhysRevE.99.062106,
title = {Generation of ice states through deep reinforcement learning},
author = {Zhao, Kai-Wen and Kao, Wen-Han and Wu, Kai-Hsin and Kao, Ying-Jer},
journal = {Phys. Rev. E},
volume = {99},
issue = {6},
pages = {062106},
numpages = {9},
year = {2019},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.99.062106},
url = {https://link.aps.org/doi/10.1103/PhysRevE.99.062106}
}
@ARTICLE{2014arXiv1410.3831M,
author = {{Mehta}, Pankaj and {Schwab}, David J.},
title = "{An exact mapping between the Variational Renormalization Group and Deep Learning}",
journal = {arXiv e-prints},
keywords = {Statistics - Machine Learning, Condensed Matter - Statistical Mechanics, Computer Science - Machine Learning, Computer Science - Neural and Evolutionary Computing},
year = 2014,
month = oct,
eid = {arXiv:1410.3831},
pages = {arXiv:1410.3831},
archivePrefix = {arXiv},
eprint = {1410.3831},
primaryClass = {stat.ML},
adsurl = {https://ui.adsabs.harvard.edu/abs/2014arXiv1410.3831M},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevB.97.045153,
title = {Machine learning spatial geometry from entanglement features},
author = {You, Yi-Zhuang and Yang, Zhao and Qi, Xiao-Liang},
journal = {Phys. Rev. B},
volume = {97},
issue = {4},
pages = {045153},
numpages = {13},
year = {2018},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.97.045153},
url = {https://link.aps.org/doi/10.1103/PhysRevB.97.045153}
}
@article{koch-janusz_mutual_2018,
title = {Mutual information, neural networks and the renormalization group},
volume = {14},
issn = {1745-2481},
url = {https://doi.org/10.1038/s41567-018-0081-4},
doi = {10.1038/s41567-018-0081-4},
abstract = {Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains ‘slow’ degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine-learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, which performs this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine-learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.},
number = {6},
journal = {Nature Physics},
author = {Koch-Janusz, Maciej and Ringel, Zohar},
month = jun,
year = {2018},
pages = {578--582},
}
@article{PhysRevE.97.053304,
title = {Scale-invariant feature extraction of neural network and renormalization group flow},
author = {Iso, Satoshi and Shiba, Shotaro and Yokoo, Sumito},
journal = {Phys. Rev. E},
volume = {97},
issue = {5},
pages = {053304},
numpages = {16},
year = {2018},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.97.053304},
url = {https://link.aps.org/doi/10.1103/PhysRevE.97.053304}
}
@article{PhysRevLett.121.260601,
title = {Neural Network Renormalization Group},
author = {Li, Shuo-Hui and Wang, Lei},
journal = {Phys. Rev. Lett.},
volume = {121},
issue = {26},
pages = {260601},
numpages = {7},
year = {2018},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.121.260601},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.260601}
}
@article{PhysRevResearch.2.023369,
title = {Machine learning holographic mapping by neural network renormalization group},
author = {Hu, Hong-Ye and Li, Shuo-Hui and Wang, Lei and You, Yi-Zhuang},
journal = {Phys. Rev. Research},
volume = {2},
issue = {2},
pages = {023369},
numpages = {12},
year = {2020},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.023369},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023369}
}
@ARTICLE{2020arXiv200600712H,
author = {{Hashimoto}, Koji and {Hu}, Hong-Ye and {You}, Yi-Zhuang},
title = "{Neural ODE and Holographic QCD}",
journal = {arXiv e-prints},
keywords = {High Energy Physics - Theory, Condensed Matter - Disordered Systems and Neural Networks, General Relativity and Quantum Cosmology, High Energy Physics - Phenomenology},
year = 2020,
month = jun,
eid = {arXiv:2006.00712},
pages = {arXiv:2006.00712},
archivePrefix = {arXiv},
eprint = {2006.00712},
primaryClass = {hep-th},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200600712H},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{2020arXiv201005703C,
author = {{Chung}, Jui-Hui and {Kao}, Ying-Jer},
title = "{Neural Monte Carlo Renormalization Group}",
journal = {arXiv e-prints},
keywords = {Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, High Energy Physics - Theory},
year = 2020,
month = oct,
eid = {arXiv:2010.05703},
pages = {arXiv:2010.05703},
archivePrefix = {arXiv},
eprint = {2010.05703},
primaryClass = {cond-mat.dis-nn},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201005703C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevX.8.031086,
title = {Reinforcement Learning in Different Phases of Quantum Control},
author = {Bukov, Marin and Day, Alexandre G. R. and Sels, Dries and Weinberg, Phillip and Polkovnikov, Anatoli and Mehta, Pankaj},
journal = {Phys. Rev. X},
volume = {8},
issue = {3},
pages = {031086},
numpages = {15},
year = {2018},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevX.8.031086},
url = {https://link.aps.org/doi/10.1103/PhysRevX.8.031086}
}
@article{PhysRevX.8.031084,
title = {Reinforcement Learning with Neural Networks for Quantum Feedback},
author = {F\"osel, Thomas and Tighineanu, Petru and Weiss, Talitha and Marquardt, Florian},
journal = {Phys. Rev. X},
volume = {8},
issue = {3},
pages = {031084},
numpages = {15},
year = {2018},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevX.8.031084},
url = {https://link.aps.org/doi/10.1103/PhysRevX.8.031084}
}
@article{PhysRevLett.122.020601,
title = {Glassy Phase of Optimal Quantum Control},
author = {Day, Alexandre G. R. and Bukov, Marin and Weinberg, Phillip and Mehta, Pankaj and Sels, Dries},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {2},
pages = {020601},
numpages = {6},
year = {2019},
month = {Jan},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.020601},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.020601}
}
@article{huembeli2018,
title = {Identifying quantum phase transitions with adversarial neural networks},
author = {Huembeli, Patrick and Dauphin, Alexandre and Wittek, Peter},
journal = {Phys. Rev. B},
volume = {97},
issue = {13},
pages = {134109},
numpages = {9},
year = {2018},
month = {Apr},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.97.134109},
url = {https://link.aps.org/doi/10.1103/PhysRevB.97.134109}
}
@article{PhysRevA.102.033326,
title = {Visualizing strange metallic correlations in the two-dimensional Fermi-Hubbard model with artificial intelligence},
author = {Khatami, Ehsan and Guardado-Sanchez, Elmer and Spar, Benjamin M. and Carrasquilla, Juan Felipe and Bakr, Waseem S. and Scalettar, Richard T.},
journal = {Phys. Rev. A},
volume = {102},
issue = {3},
pages = {033326},
numpages = {11},
year = {2020},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.102.033326},
url = {https://link.aps.org/doi/10.1103/PhysRevA.102.033326}
}
@article{chng2017,
title = {Machine Learning Phases of Strongly Correlated Fermions},
author = {Ch'ng, Kelvin and Carrasquilla, Juan and Melko, Roger G. and Khatami, Ehsan},
journal = {Phys. Rev. X},
volume = {7},
issue = {3},
pages = {031038},
numpages = {9},
year = {2017},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevX.7.031038},
url = {https://link.aps.org/doi/10.1103/PhysRevX.7.031038}
}
@article{PhysRevLett.125.127401,
title = {Identifying Topological Phase Transitions in Experiments Using Manifold Learning},
author = {Lustig, Eran and Yair, Or and Talmon, Ronen and Segev, Mordechai},
journal = {Phys. Rev. Lett.},
volume = {125},
issue = {12},
pages = {127401},
numpages = {6},
year = {2020},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.125.127401},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.127401}
}
@article{rodriguez-nieva2019,
title = {Identifying Topological Order through Unsupervised Machine Learning},
author = {{Rodriguez-Nieva}, Joaquin F. and Scheurer, Mathias S.},
year = {2019},
month = aug,
volume = {15},
pages = {790--795},
issn = {1745-2481},
doi = {10.1038/s41567-019-0512-x},
abstract = {Machine learning techniques have latterly gained currency in condensed-matter physics, for example by identifying phase transitions. An unsupervised machine learning algorithm that identifies topological order is now demonstrated.},
copyright = {2019 The Author(s), under exclusive licence to Springer Nature Limited},
journal = {Nature Physics},
number = {8}
}
@article{broecker2017b,
title = {Quantum Phase Recognition via Unsupervised Machine Learning},
author = {Broecker, Peter and Assaad, Fakher F. and Trebst, Simon},
year = {2017},
month = jul,
abstract = {The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or the ensemble of correlators sampled in Monte Carlo simulations. Here we introduce a gener- alization of supervised machine learning approaches that allows to accurately map out phase diagrams of inter- acting many-body systems without any prior knowledge, e.g. of their general topology or the number of distinct phases. To substantiate the versatility of this approach, which combines convolutional neural networks with quantum Monte Carlo sampling, we map out the phase diagrams of interacting boson and fermion models both at zero and finite temperatures and show that first-order, second-order, and Kosterlitz-Thouless phase transitions can all be identified. We explicitly demonstrate that our approach is capable of identifying the phase transition to non-trivial many-body phases such as superfluids or topologically ordered phases without supervision.},
archivePrefix = {arXiv},
eprint = {1707.00663},
eprinttype = {arxiv},
journal = {arXiv:1707.00663 [cond-mat]},
keywords = {Condensed Matter - Disordered Systems and Neural Networks,Condensed Matter - Statistical Mechanics,Condensed Matter - Strongly Correlated Electrons},
primaryClass = {cond-mat}
}
@article{broecker2017,
title = {Machine learning quantum phases of matter beyond the fermion sign problem},
volume = {7},
issn = {2045-2322},
url = {https://doi.org/10.1038/s41598-017-09098-0},
doi = {10.1038/s41598-017-09098-0},
abstract = {State-of-the-art machine learning techniques promise to become a powerful tool in statistical mechanics via their capacity to distinguish different phases of matter in an automated way. Here we demonstrate that convolutional neural networks (CNN) can be optimized for quantum many-fermion systems such that they correctly identify and locate quantum phase transitions in such systems. Using auxiliary-field quantum Monte Carlo (QMC) simulations to sample the many-fermion system, we show that the Green’s function holds sufficient information to allow for the distinction of different fermionic phases via a CNN. We demonstrate that this QMC + machine learning approach works even for systems exhibiting a severe fermion sign problem where conventional approaches to extract information from the Green’s function, e.g. in the form of equal-time correlation functions, fail.},
number = {1},
journal = {Scientific Reports},
author = {Broecker, Peter and Carrasquilla, Juan and Melko, Roger G. and Trebst, Simon},
month = aug,
year = {2017},
pages = {8823},
}
@ARTICLE{2020arXiv201003655Y,
author = {{Yao}, Jiahao and {Lin}, Lin and {Bukov}, Marin},
title = "{Reinforcement Learning for Many-Body Ground State Preparation based on Counter-Diabatic Driving}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Quantum Gases, Computer Science - Machine Learning, Physics - Computational Physics},
year = 2020,
month = oct,
eid = {arXiv:2010.03655},
pages = {arXiv:2010.03655},
archivePrefix = {arXiv},
eprint = {2010.03655},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201003655Y},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{eun-ah2017,
title = {Quantum Loop Topography for Machine Learning},
author = {Zhang, Yi and Kim, Eun-Ah},
journal = {Phys. Rev. Lett.},
volume = {118},
issue = {21},
pages = {216401},
numpages = {5},
year = {2017},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.118.216401},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.118.216401}
}
@article{dassarma2017,
title = {Machine learning topological states},
author = {Deng, Dong-Ling and Li, Xiaopeng and Das Sarma, S.},
journal = {Phys. Rev. B},
volume = {96},
issue = {19},
pages = {195145},
numpages = {11},
year = {2017},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.96.195145},
url = {https://link.aps.org/doi/10.1103/PhysRevB.96.195145}
}
@article{neupeurt2017,
title = {Probing many-body localization with neural networks},
author = {Schindler, Frank and Regnault, Nicolas and Neupert, Titus},
journal = {Phys. Rev. B},
volume = {95},
issue = {24},
pages = {245134},
numpages = {11},
year = {2017},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.95.245134},
url = {https://link.aps.org/doi/10.1103/PhysRevB.95.245134}
}
@article{yi-ting2018,
title = {Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal},
author = {Hsu, Yi-Ting and Li, Xiao and Deng, Dong-Ling and Das Sarma, S.},
journal = {Phys. Rev. Lett.},
volume = {121},
issue = {24},
pages = {245701},
numpages = {6},
year = {2018},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.121.245701},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.121.245701}
}
@misc{tensorflow,
title={{TensorFlow}: Large-Scale Machine Learning on Heterogeneous Systems},
url={http://tensorflow.org/},
note={Software available from tensorflow.org},
author={
Mart\'{\i}n~Abadi and
Ashish~Agarwal and
Paul~Barham and
Eugene~Brevdo and
Zhifeng~Chen and
Craig~Citro and
Greg~S.~Corrado and
Andy~Davis and
Jeffrey~Dean and
Matthieu~Devin and
Sanjay~Ghemawat and
Ian~Goodfellow and
Andrew~Harp and
Geoffrey~Irving and
Michael~Isard and
Yangqing Jia and
Rafal~Jozefowicz and
Lukasz~Kaiser and
Manjunath~Kudlur and
Josh~Levenberg and
Dan~Man\'{e} and
Rajat~Monga and
Sherry~Moore and
Derek~Murray and
Chris~Olah and
Mike~Schuster and
Jonathon~Shlens and
Benoit~Steiner and
Ilya~Sutskever and
Kunal~Talwar and
Paul~Tucker and
Vincent~Vanhoucke and
Vijay~Vasudevan and
Fernanda~Vi\'{e}gas and
Oriol~Vinyals and
Pete~Warden and
Martin~Wattenberg and
Martin~Wicke and
Yuan~Yu and
Xiaoqiang~Zheng},
year={2015},
}
@ARTICLE{itensor,
author = {{Fishman}, Matthew and {White}, Steven R. and {Miles Stoudenmire}, E.},
title = "{The ITensor Software Library for Tensor Network Calculations}",
journal = {arXiv e-prints},
keywords = {Computer Science - Mathematical Software, Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics},
year = 2020,
month = jul,
eid = {arXiv:2007.14822},
pages = {arXiv:2007.14822},
archivePrefix = {arXiv},
eprint = {2007.14822},
primaryClass = {cs.MS},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200714822F},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Endres2016,
abstract = {The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a platform for the deterministic preparation of regular one-dimensional arrays of individually controlled cold atoms. In our approach, a measurement and feedback procedure emiliminates the entropy associated with probabilistic trap occupation and results in defect-free arrays of over 50 atoms in less than 400 milliseconds. The technique is based on fast, real-time control of 100 optical tweezers, which we use to arrange atoms in desired geometric patterns and to maintain these configurations by replacing lost atoms with surplus atoms from a reservoir. This bottom-up approach may enable controlled engineering of scalable many-body systems for quantum information processing, quantum simulations, and precision measurements.},
author = {Endres, Manuel and Bernien, Hannes and Keesling, Alexander and Levine, Harry and Anschuetz, Eric R and Krajenbrink, Alexandre and Senko, Crystal and Vuletic, Vladan and Greiner, Markus and Lukin, Mikhail D},
doi = {10.1126/science.aah3752},
issn = {0036-8075},
journal = {Science},
month = {nov},
number = {6315},
pages = {1024--1027},
publisher = {American Association for the Advancement of Science},
title = {{Atom-by-atom assembly of defect-free one-dimensional cold atom arrays}},
url = {http://www.sciencemag.org/lookup/doi/10.1126/science.aah3752},
volume = {354},
year = {2016}
}
@article{Keesling2018,
abstract = {Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.},
archivePrefix = {arXiv},
arxivId = {1809.05540},
author = {Keesling, Alexander and Omran, Ahmed and Levine, Harry and Bernien, Hannes and Pichler, Hannes and Choi, Soonwon and Samajdar, Rhine and Schwartz, Sylvain and Silvi, Pietro and Sachdev, Subir and Zoller, Peter and Endres, Manuel and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.},
eprint = {1809.05540},
keywords = {Keesling2018},
mendeley-tags = {Keesling2018},
month = {sep},
title = {{Probing quantum critical dynamics on a programmable Rydberg simulator}},
url = {http://arxiv.org/abs/1809.05540},
year = {2018}
}
@article{keesling_quantum_2019,
title = {Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulator},
volume = {568},
issn = {1476-4687},
url = {https://doi.org/10.1038/s41586-019-1070-1},
doi = {10.1038/s41586-019-1070-1},
number = {7751},
journal = {Nature},
author = {Keesling, Alexander and Omran, Ahmed and Levine, Harry and Bernien, Hannes and Pichler, Hannes and Choi, Soonwon and Samajdar, Rhine and Schwartz, Sylvain and Silvi, Pietro and Sachdev, Subir and Zoller, Peter and Endres, Manuel and Greiner, Markus and Vuletic, Vladan and Lukin, Mikhail D.},
month = apr,
year = {2019},
pages = {207--211},
}
@article{Bernien2017,
annote = {Article},
author = {Bernien, Hannes and Schwartz, Sylvain and Keesling, Alexander and Levine, Harry and Omran, Ahmed and Pichler, Hannes and Choi, Soonwon and Zibrov, Alexander S and Endres, Manuel and Greiner, Markus and Vuleti{\'{c}}, Vladan and Lukin, Mikhail D},
doi = {10.1038/nature24622},
issn = {0028-0836},
journal = {Nature},
month = {nov},
number = {7682},
pages = {579--584},
publisher = {Macmillan Publishers Limited, part of Springer Nature. All rights reserved. SN -},
title = {{Probing many-body dynamics on a 51-atom quantum simulator}},
url = {http://dx.doi.org/10.1038/nature24622 http://www.nature.com/doifinder/10.1038/nature24622},
volume = {551},
year = {2017}
}
@article{Labuhn,
Author = {Labuhn, Henning and Barredo, Daniel and Ravets, Sylvain and de L{\'e}s{\'e}leuc, Sylvain and Macr{\`\i}, Tommaso and Lahaye, Thierry and Browaeys, Antoine},
Date = {2016/06/01/online},
Date-Added = {2019-03-29 14:59:41 +0000},
Date-Modified = {2019-03-29 14:59:41 +0000},
Day = {01},
Journal = {Nature},
L3 = {10.1038/nature18274; },
Month = {06},
Pages = {667 EP -},
Publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved. SN -},
Title = {Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models},
Ty = {JOUR},
Url = {https://doi.org/10.1038/nature18274},
Volume = {534},
Year = {2016},
Bdsk-Url-1 = {https://doi.org/10.1038/nature18274}}
@article {Omran570,
author = {Omran, A. and Levine, H. and Keesling, A. and Semeghini, G. and Wang, T. T. and Ebadi, S. and Bernien, H. and Zibrov, A. S. and Pichler, H. and Choi, S. and Cui, J. and Rossignolo, M. and Rembold, P. and Montangero, S. and Calarco, T. and Endres, M. and Greiner, M. and Vuleti{\'c}, V. and Lukin, M. D.},
title = {Generation and manipulation of Schr{\"o}dinger cat states in Rydberg atom arrays},
volume = {365},
number = {6453},
pages = {570--574},
year = {2019},
doi = {10.1126/science.aax9743},
publisher = {American Association for the Advancement of Science},
abstract = {The success of quantum computing relies on the ability to entangle large-scale systems. Various platforms are being pursued, with architectures based on superconducting qubits and trapped atoms being the most advanced. By entangling up to 20 qubits, Omran et al. and Song et al.{\textemdash}working with Rydberg atom qubits and superconducting qubits, respectively{\textemdash}demonstrate how far these platforms have reached. The demonstrated controllable generation and detection of entanglement on such quantum systems is promising for the development of large-scale quantum processors.Science, this issue p. 570, p. 574Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of {\textquotedblleft}Schr{\"o}dinger cat{\textquotedblright} states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.},
issn = {0036-8075},
URL = {https://science.sciencemag.org/content/365/6453/570},
eprint = {https://science.sciencemag.org/content/365/6453/570.full.pdf},
journal = {Science}
}
@inproceedings{cho-etal-2014-learning,
title = "Learning Phrase Representations using {RNN} Encoder{--}Decoder for Statistical Machine Translation",
author = {Cho, Kyunghyun and
van Merri{\"e}nboer, Bart and
Gulcehre, Caglar and
Bahdanau, Dzmitry and
Bougares, Fethi and
Schwenk, Holger and
Bengio, Yoshua},
booktitle = "Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing ({EMNLP})",
month = oct,
year = "2014",
address = "Doha, Qatar",
publisher = "Association for Computational Linguistics",
url = "https://www.aclweb.org/anthology/D14-1179",
doi = "10.3115/v1/D14-1179",
pages = "1724--1734",
}
@article{Levine2019,
title = {Parallel Implementation of High-Fidelity Multiqubit Gates with Neutral Atoms},
author = {Levine, Harry and Keesling, Alexander and Semeghini, Giulia and Omran, Ahmed and Wang, Tout T. and Ebadi, Sepehr and Bernien, Hannes and Greiner, Markus and Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Vladan and Pichler, Hannes and Lukin, Mikhail D.},
journal = {Phys. Rev. Lett.},
volume = {123},
issue = {17},
pages = {170503},
numpages = {6},
year = {2019},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.123.170503},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.170503}
}
@article {Schauss1455,
author = {Schau{\ss}, P. and Zeiher, J. and Fukuhara, T. and Hild, S. and Cheneau, M. and Macr{\`\i}, T. and Pohl, T. and Bloch, I. and Gross, C.},
title = {Crystallization in Ising quantum magnets},
volume = {347},
number = {6229},
pages = {1455--1458},
year = {2015},
doi = {10.1126/science.1258351},
publisher = {American Association for the Advancement of Science},
abstract = {In physics, interactions between components of a system can cause it to become more orderly in an attempt to minimize energy. Such ordered phases appear, for example, in magnetic systems. Schauss et al. simulated these phenomena using a collection of neutral atoms at low temperatures. By shining laser light on the atoms, the authors brought some of them into a high energy state called the Rydberg state. By carefully varying the experimental parameters, they coaxed these Rydberg atoms into patterns reminiscent of crystal lattices in rod- and disk-shaped atomic samples.Science, this issue p. 1455 Dominating finite-range interactions in many-body systems can lead to intriguing self-ordered phases of matter. For quantum magnets, Ising models with power-law interactions are among the most elementary systems that support such phases. These models can be implemented by laser coupling ensembles of ultracold atoms to Rydberg states. Here, we report on the experimental preparation of crystalline ground states of such spin systems. We observe a magnetization staircase as a function of the system size and show directly the emergence of crystalline states with vanishing susceptibility. Our results demonstrate the precise control of Rydberg many-body systems and may enable future studies of phase transitions and quantum correlations in interacting quantum magnets.},
issn = {0036-8075},
journal = {Science}
}
@article{Kullback:1951aa,
Author = {Kullback, S. and Leibler, R. A.},
Da = {1951/03},
Date-Added = {2020-05-06 19:36:51 +0000},
Date-Modified = {2020-05-06 19:36:51 +0000},
Doi = {10.1214/aoms/1177729694},
Isbn = {0003-4851},
Journal = {Ann. Math. Statist.},
La = {en},
Number = {1},
Pages = {79--86},
Publisher = {The Institute of Mathematical Statistics},
Title = {On Information and Sufficiency},
Ty = {JOUR},
Url = {https://projecteuclid.org:443/euclid.aoms/1177729694},
Volume = {22},
Year = {1951},
Bdsk-Url-1 = {https://projecteuclid.org:443/euclid.aoms/1177729694},
Bdsk-Url-2 = {https://doi.org/10.1214/aoms/1177729694}}
@book{nielsen_chuang_2010, place={Cambridge}, title={Quantum Computation and Quantum Information: 10th Anniversary Edition}, DOI={10.1017/CBO9780511976667}, publisher={Cambridge University Press}, author={Nielsen, Michael A. and Chuang, Isaac L.}, year={2010}}
@article{annurev-conmatphys-031119-050651,
author = {Torlai, Giacomo and Melko, Roger G.},
title = {Machine-Learning Quantum States in the NISQ Era},
journal = {Annual Review of Condensed Matter Physics},
volume = {11},
number = {1},
pages = {325-344},
year = {2020},
doi = {10.1146/annurev-conmatphys-031119-050651},
URL = {
https://doi.org/10.1146/annurev-conmatphys-031119-050651
},
eprint = {
https://doi.org/10.1146/annurev-conmatphys-031119-050651
}
,
abstract = { We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. We review recent techniques in reconstruction of a cold atom wavefunction, intended for use on experimental noisy intermediate-scale quantum (NISQ) devices. Finally, we discuss the outlook for future experimental state reconstruction using machine learning in the NISQ era and beyond. }
}
@article{LeCun2015,
abstract = {Deep learning},
author = {LeCun, Yann and Bengio, Yoshua and Hinton, Geoffrey},
doi = {10.1038/nature14539},
file = {:Users/btimar/Library/Application Support/Mendeley Desktop/Downloaded/LeCun, Bengio, Hinton - 2015 - Deep learning.pdf:pdf},
issn = {0028-0836},
journal = {Nature},
keywords = {Computer science,Mathematics and computing},
month = {may},
number = {7553},
pages = {436--444},
publisher = {Nature Publishing Group},
title = {{Deep learning}},
url = {http://www.nature.com/articles/nature14539},
volume = {521},
year = {2015}
}
@article{Little78,
title = "Analytic study of the memory storage capacity of a neural network",
journal = "Mathematical Biosciences",
volume = "39",
number = "3",
pages = "281 - 290",
year = "1978",
issn = "0025-5564",
doi = "https://doi.org/10.1016/0025-5564(78)90058-5",
url = "http://www.sciencedirect.com/science/article/pii/0025556478900585",
author = "W.A. Little and Gordon L. Shaw",
abstract = "Previously, we developed a model of short and long term memory which was based on an analogy to the Ising spin system in a neural network. We assumed that the modification of the synaptic strengths was dependent upon the correlation of pre- and post-synaptic neuronal firing. This assumption we denote as the Hebb hypothesis. In this paper, we solve exactly a linearized version of the model and explicitly show that the capacity of the memory is related to the number of synapses rather than the much smaller number of neurons. In addition, we show that in order to utilize this large capacity, the network must store the major part of the information in the capability to generate patterns which evolve with time. We are also led to a modified Hebb hypothesis."
}
@article{Little74,
title = "The existence of persistent states in the brain",
journal = "Mathematical Biosciences",
volume = "19",
number = "1",
pages = "101 - 120",
year = "1974",
issn = "0025-5564",
doi = "https://doi.org/10.1016/0025-5564(74)90031-5",
url = "http://www.sciencedirect.com/science/article/pii/0025556474900315",
author = "W.A. Little",
abstract = "We show that given certain plausible assumptions the existence of persistent states in a neural network can occur only if a certain transfer matrix has degenerate maximum eigenvalues. The existence of such states of persistent order is directly analogous to the existence of long range order in an Ising spin system; while the transition to the state of persistent order is analogous to the transition to the ordered phase of the spin system. It is shown that the persistent state is also characterized by correlations between neurons throughout the brain. It is suggested that these persistent states are associated with short term memory while the eigenvectors of the transfer matrix are a representation of long term memory. A numerical example is given that illustrates certain of these features."
}
@article{niu_universal_2019,
title = {Universal Quantum Control through Deep Reinforcement Learning},
author = {Niu, Murphy Yuezhen and Boixo, Sergio and Smelyanskiy, Vadim N. and Neven, Hartmut},
year = {2019},
month = apr,
volume = {5},
pages = {1--8},
issn = {2056-6387},
doi = {10.1038/s41534-019-0141-3},
abstract = {Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To leverage these powerful capabilities for quantum control optimization, we propose a new control framework to simultaneously optimize the speed and fidelity of quantum computation against both leakage and stochastic control errors. For a broad family of two-qubit unitary gates that are important for quantum simulation of many-electron systems, we improve the control robustness by adding control noise into training environments for reinforcement learning agents trained with trusted-region-policy-optimization. The agent control solutions demonstrate a two-order-of-magnitude reduction in average-gate-error over baseline stochastic-gradient-descent solutions and up to a one-order-of-magnitude reduction in gate time from optimal gate synthesis counterparts. These significant improvements in both fidelity and runtime are achieved by combining new physical understandings and state-of-the-art machine learning techniques. Our results open a venue for wider applications in quantum simulation, quantum chemistry and quantum supremacy tests using near-term quantum devices.},
copyright = {2019 The Author(s)},
journal = {npj Quantum Information},
number = {1}
}
@article{coopmans2020,
title = {Protocol {{Discovery}} for the {{Quantum Control}} of {{Majoranas}} by {{Differential Programming}} and {{Natural Evolution Strategies}}},
author = {Coopmans, Luuk and Luo, Di and Kells, Graham and Clark, Bryan K. and Carrasquilla, Juan},
year = {2020},
month = aug,
abstract = {Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology. Here we apply Differentiable Programming (DP) and Natural Evolution Strategies (NES) to the optimal transport of Majorana zero modes in large superconducting nano-wires, a key element to the success of Majorana-based topological quantum computation. We formulate the motion control of Majorana fermions as an optimization problem for which we propose a new categorization of four different regimes with respect to the critical velocity of the system and the total transport time. In addition to correctly recovering the anticipated smooth protocols in the adiabatic regime, our algorithms uncover efficient but strikingly counter-intuitive motion strategies in the non-adiabatic regime. The emergent picture reveals a simple but high fidelity strategy that makes use of pulse-like jumps at the beginning and the end of the protocol with a period of constant velocity in between the jumps, which we dub the jump-move-jump protocol. We provide a transparent semi-analytical picture, which uses the sudden approximation and a reformulation of the Majorana motion in a moving frame, to illuminate the key characteristics of the jump-move-jump control strategy. Our results demonstrate that machine learning for quantum control can be applied efficiently to quantum many-body dynamical systems with performance levels that make it relevant to the realization of large-scale quantum technology.},
archivePrefix = {arXiv},
eprint = {2008.09128},
eprinttype = {arxiv},
journal = {arXiv:2008.09128 [cond-mat, physics:physics, physics:quant-ph]},
keywords = {Condensed Matter - Strongly Correlated Electrons,Physics - Computational Physics,Quantum Physics},
primaryClass = {cond-mat, physics:physics, physics:quant-ph}
}
@article{bukov2018,
title = {Reinforcement {{Learning}} in {{Different Phases}} of {{Quantum Control}}},
author = {Bukov, Marin and Day, Alexandre G. R. and Sels, Dries and Weinberg, Phillip and Polkovnikov, Anatoli and Mehta, Pankaj},
year = {2018},
month = sep,
volume = {8},
pages = {031086},
doi = {10.1103/PhysRevX.8.031086},
abstract = {The ability to prepare a physical system in a desired quantum state is central to many areas of physics such as nuclear magnetic resonance, cold atoms, and quantum computing. Yet, preparing states quickly and with high fidelity remains a formidable challenge. In this work, we implement cutting-edge reinforcement learning (RL) techniques and show that their performance is comparable to optimal control methods in the task of finding short, high-fidelity driving protocol from an initial to a target state in nonintegrable many-body quantum systems of interacting qubits. RL methods learn about the underlying physical system solely through a single scalar reward (the fidelity of the resulting state) calculated from numerical simulations of the physical system. We further show that quantum-state manipulation viewed as an optimization problem exhibits a spin-glass-like phase transition in the space of protocols as a function of the protocol duration. Our RL-aided approach helps identify variational protocols with nearly optimal fidelity, even in the glassy phase, where optimal state manipulation is exponentially hard. This study highlights the potential usefulness of RL for applications in out-of-equilibrium quantum physics.},
journal = {Physical Review X},
number = {3}
}
@book{PDP,
editor = {Rumelhart, David E. and McClelland, James L.},
title = {Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1: Foundations},
year = {1986},
isbn = {0-262-68053-X},
source = {softcover, \$21.95},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
}
@article {Hopfield82,
author = {Hopfield, J J},
title = {Neural networks and physical systems with emergent collective computational abilities},
volume = {79},
number = {8},
pages = {2554--2558},
year = {1982},
doi = {10.1073/pnas.79.8.2554},
publisher = {National Academy of Sciences},
abstract = {Computational properties of use of biological organisms or to the construction of computers can emerge as collective properties of systems having a large number of simple equivalent components (or neurons). The physical meaning of content-addressable memory is described by an appropriate phase space flow of the state of a system. A model of such a system is given, based on aspects of neurobiology but readily adapted to integrated circuits. The collective properties of this model produce a content-addressable memory which correctly yields an entire memory from any subpart of sufficient size. The algorithm for the time evolution of the state of the system is based on asynchronous parallel processing. Additional emergent collective properties include some capacity for generalization, familiarity recognition, categorization, error correction, and time sequence retention. The collective properties are only weakly sensitive to details of the modeling or the failure of individual devices.},
issn = {0027-8424},
journal = {Proceedings of the National Academy of Sciences}
}
@article{HintonBackProp,
Author = {Rumelhart, David E. and Hinton, Geoffrey E. and Williams, Ronald J.},
Date = {1986/10/09/online},
Date-Added = {2018-09-17 04:18:45 +0000},
Date-Modified = {2018-09-17 04:18:45 +0000},
Day = {09},
Journal = {Nature},
L3 = {10.1038/323533a0; },
Month = {10},
Pages = {533 EP -},
Publisher = {Nature Publishing Group SN -},
Title = {Learning representations by back-propagating errors},
Ty = {JOUR},
Url = {http://dx.doi.org/10.1038/323533a0},
Volume = {323},
Year = {1986},
Bdsk-Url-1 = {http://dx.doi.org/10.1038/323533a0}}
@article{Ackley85,
title = "A learning algorithm for boltzmann machines",
journal = "Cognitive Science",
volume = "9",
number = "1",
pages = "147 - 169",
year = "1985",
issn = "0364-0213",
doi = "https://doi.org/10.1016/S0364-0213(85)80012-4",
url = "http://www.sciencedirect.com/science/article/pii/S0364021385800124",
author = "David H. Ackley and Geoffrey E. Hinton and Terrence J. Sejnowski",
abstract = "The computational power of massively parallel networks of simple processing elements resides in the communication bandwidth provided by the hardware connections between elements. These connections can allow a significant fraction of the knowledge of the system to be applied to an instance of a problem in a very short time. One kind of computation for which massively parallel networks appear to be well suited is large constraint satisfaction searches, but to use the connections efficiently two conditions must be met: First, a search technique that is suitable for parallel networks must be found. Second, there must be some way of choosing internal representations which allow the preexisting hardware connections to be used efficiently for encoding the constraints in the domain being searched. We describe a general parallel search method, based on statistical mechanics, and we show how it leads to a general learning rule for modifying the connection strengths so as to incorporate knowledge about a task domain in an efficient way. We describe some simple examples in which the learning algorithm creates internal representations that are demonstrably the most efficient way of using the preexisting connectivity structure."
}
@article{McCullogh43,
Author = {McCulloch, Warren S. and Pitts, Walter},
Da = {1943/12/01},
Date-Added = {2018-09-01 22:18:47 +0000},
Date-Modified = {2018-09-01 22:18:47 +0000},
Doi = {10.1007/BF02478259},
Id = {McCulloch1943},
Isbn = {1522-9602},
Journal = {The bulletin of mathematical biophysics},
Number = {4},
Pages = {115--133},
Title = {A logical calculus of the ideas immanent in nervous activity},
Ty = {JOUR},
Url = {https://doi.org/10.1007/BF02478259},
Volume = {5},
Year = {1943},
Bdsk-Url-1 = {https://doi.org/10.1007/BF02478259},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/BF02478259}}
@article {Melnikov1221,
author = {Melnikov, Alexey A. and Poulsen Nautrup, Hendrik and Krenn, Mario and Dunjko, Vedran and Tiersch, Markus and Zeilinger, Anton and Briegel, Hans J.},
title = {Active learning machine learns to create new quantum experiments},
volume = {115},
number = {6},
pages = {1221--1226},
year = {2018},
doi = {10.1073/pnas.1714936115},
publisher = {National Academy of Sciences},
abstract = {Quantum experiments push the envelope of our understanding of fundamental concepts in quantum physics. Modern experiments have exhaustively probed the basic notions of quantum theory. Arguably, further breakthroughs require the tackling of complex quantum phenomena and consequently require complex experiments and involved techniques. The designing of such complex experiments is difficult and often clashes with human intuition. We present an autonomous learning model which learns to design such complex experiments, without relying on previous knowledge or often flawed intuition. Our system not only learns how to design desired experiments more efficiently than the best previous approaches, but in the process also discovers nontrivial experimental techniques. Our work demonstrates that learning machines can offer dramatic advances in how experiments are generated.How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of various entanglement classes in quantum experiments. We investigate this question by using the projective simulation model, a physics-oriented approach to artificial intelligence. In our approach, the projective simulation system is challenged to design complex photonic quantum experiments that produce high-dimensional entangled multiphoton states, which are of high interest in modern quantum experiments. The artificial intelligence system learns to create a variety of entangled states and improves the efficiency of their realization. In the process, the system autonomously (re)discovers experimental techniques which are only now becoming standard in modern quantum optical experiments{\textemdash}a trait which was not explicitly demanded from the system but emerged through the process of learning. Such features highlight the possibility that machines could have a significantly more creative role in future research.},
issn = {0027-8424},
URL = {https://www.pnas.org/content/115/6/1221},
eprint = {https://www.pnas.org/content/115/6/1221.full.pdf},
journal = {Proceedings of the National Academy of Sciences}
}
@article{Dunjko_2018,
doi = {10.1088/1361-6633/aab406},
url = {https://doi.org/10.1088%2F1361-6633%2Faab406},
year = 2018,
month = {jun},
publisher = {{IOP} Publishing},
volume = {81},
number = {7},
pages = {074001},
author = {Vedran Dunjko and Hans J Briegel},
title = {Machine learning {\&} artificial intelligence in the quantum domain: a review of recent progress},
journal = {Reports on Progress in Physics},
abstract = {Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research—quantum information versus machine learning (ML) and artificial intelligence (AI)—have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our ‘big data’ world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement—exploring what ML/AI can do for quantum physics and vice versa—researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.}
}
@article{Rosenblatt58,
added-at = {2009-10-27T06:49:28.000+0100},
author = {Rosenblatt, Frank},
biburl = {https://www.bibsonomy.org/bibtex/2afcce29c2471aaa8480d2c2159361e88/chrmina},
journal = {Psychological Review},
keywords = {imported},
number = 6,
pages = {386-408},
timestamp = {2009-10-27T06:49:30.000+0100},
title = {The Perceptron: A Probabilistic Model for Information Storage and Organization in the Brain},
volume = 65,
year = 1958
}
@article{doi:10.1080/23746149.2020.1797528,
author = { Juan Carrasquilla },
title = {Machine learning for quantum matter},
journal = {Advances in Physics: X},
volume = {5},
number = {1},
pages = {1797528},
year = {2020},
publisher = {Taylor & Francis},
doi = {10.1080/23746149.2020.1797528},
URL = {
https://doi.org/10.1080/23746149.2020.1797528
},
eprint = {
https://doi.org/10.1080/23746149.2020.1797528
}
}
@book{10.5555/551283,
author = {Sutton, Richard S. and Barto, Andrew G.},
title = {Introduction to Reinforcement Learning},
year = {1998},
isbn = {0262193981},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
edition = {1st}
}
@book{10.5555/1162264,
author = {Bishop, Christopher M.},
title = {Pattern Recognition and Machine Learning (Information Science and Statistics)},
year = {2006},
isbn = {0387310738},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg}
}
@article{Samajdar2020,
title = {Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays},
author = {Samajdar, Rhine and Ho, Wen Wei and Pichler, Hannes and Lukin, Mikhail D. and Sachdev, Subir},
journal = {Phys. Rev. Lett.},
volume = {124},
issue = {10},
pages = {103601},
numpages = {7},
year = {2020},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.124.103601},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.103601}
}
@article{RevModPhys.91.045002,
title = {Machine learning and the physical sciences},
author = {Carleo, Giuseppe and Cirac, Ignacio and Cranmer, Kyle and Daudet, Laurent and Schuld, Maria and Tishby, Naftali and Vogt-Maranto, Leslie and Zdeborov\'a, Lenka},
journal = {Rev. Mod. Phys.},
volume = {91},
issue = {4},
pages = {045002},
numpages = {39},
year = {2019},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/RevModPhys.91.045002},
url = {https://link.aps.org/doi/10.1103/RevModPhys.91.045002}
}
@article{SCHOLLWOCK201196,
title = "The density-matrix renormalization group in the age of matrix product states",
journal = "Annals of Physics",
volume = "326",
number = "1",
pages = "96 - 192",
year = "2011",
note = "January 2011 Special Issue",
issn = "0003-4916",
doi = "https://doi.org/10.1016/j.aop.2010.09.012",
url = "http://www.sciencedirect.com/science/article/pii/S0003491610001752",
author = "Ulrich Schollwoeck",
abstract = "The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensional strongly correlated quantum lattice systems. In the further development of the method, the realization that DMRG operates on a highly interesting class of quantum states, so-called matrix product states (MPS), has allowed a much deeper understanding of the inner structure of the DMRG method, its further potential and its limitations. In this paper, I want to give a detailed exposition of current DMRG thinking in the MPS language in order to make the advisable implementation of the family of DMRG algorithms in exclusively MPS terms transparent. I then move on to discuss some directions of potentially fruitful further algorithmic development: while DMRG is a very mature method by now, I still see potential for further improvements, as exemplified by a number of recently introduced algorithms."
}
@article{PhysRevB.48.10345,
title = {Density-matrix algorithms for quantum renormalization groups},
author = {White, Steven R.},
journal = {Phys. Rev. B},
volume = {48},
issue = {14},
pages = {10345--10356},
numpages = {0},
year = {1993},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.48.10345},
url = {https://link.aps.org/doi/10.1103/PhysRevB.48.10345}
}
@incollection{Smolensky1986,
author = {Smolensky, P.},
chapter = {Information Processing in Dynamical Systems: Foundations of Harmony Theory},
title = {Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Vol. 1},
editor = {Rumelhart, David E. and McClelland, James L. and PDP Research Group, CORPORATE},
booktitle={Parallel Distributed Processing},
year = {1986},
isbn = {0-262-68053-X},
pages = {194--281},
numpages = {88},
url = {http://dl.acm.org/citation.cfm?id=104279.104290},
acmid = {104290},
publisher = {MIT Press},
address = {Cambridge, MA, USA},
}
@article{PhysRevLett.69.2863,
title = {Density matrix formulation for quantum renormalization groups},
author = {White, Steven R.},
journal = {Phys. Rev. Lett.},
volume = {69},
issue = {19},
pages = {2863--2866},
numpages = {0},
year = {1992},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.69.2863},
url = {https://link.
aps.org/doi/10.1103/PhysRevLett.69.2863}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QEC
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{torlai_neural_2016,
title = {Neural Decoder for Topological Codes},
author = {Torlai, Giacomo and Melko, Roger G.},
journal = {Phys. Rev. Lett.},
volume = {119},
issue = {3},
pages = {030501},
numpages = {5},
year = {2017},
month = {Jul},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.119.030501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.119.030501}
}
@article{krastanov_deep_2017,
title = {Deep {Neural} {Network} {Probabilistic} {Decoder} for {Stabilizer} {Codes}},
volume = {7},
issn = {2045-2322},
url = {https://doi.org/10.1038/s41598-017-11266-1},
doi = {10.1038/s41598-017-11266-1},
abstract = {Neural networks can efficiently encode the probability distribution of errors in an error correcting code. Moreover, these distributions can be conditioned on the syndromes of the corresponding errors. This paves a path forward for a decoder that employs a neural network to calculate the conditional distribution, then sample from the distribution - the sample will be the predicted error for the given syndrome. We present an implementation of such an algorithm that can be applied to any stabilizer code. Testing it on the toric code, it has higher threshold than a number of known decoders thanks to naturally finding the most probable error and accounting for correlations between errors.},
number = {1},
journal = {Scientific Reports},
author = {Krastanov, Stefan and Jiang, Liang},
month = sep,
year = {2017},
pages = {11003},
}
@article{Varsamopoulos_2017,
doi = {10.1088/2058-9565/aa955a},
url = {https://doi.org/10.1088%2F2058-9565%2Faa955a},
year = 2017,
month = {nov},
publisher = {{IOP} Publishing},
volume = {3},
number = {1},
pages = {015004},
author = {Savvas Varsamopoulos and Ben Criger and Koen Bertels},
title = {Decoding small surface codes with feedforward neural networks},
journal = {Quantum Science and Technology},
abstract = {Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the decoding problem to a classification problem that a feedforward neural network can solve. We investigate quantum error correction and fault tolerance at small code distances using neural network-based decoders, demonstrating that the neural network can generalize to inputs that were not provided during training and that they can reach similar or better decoding performance compared to previous algorithms. We conclude by discussing the time required by a feedforward neural network decoder in hardware.}
}
@article{Baireuther2018machinelearning,
doi = {10.22331/q-2018-01-29-48},
url = {https://doi.org/10.22331/q-2018-01-29-48},
title = {Machine-learning-assisted correction of correlated qubit errors in a topological code},
author = {Baireuther, Paul and O'Brien, Thomas E. and Tarasinski, Brian and Beenakker, Carlo W. J.},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {2},
pages = {48},
month = jan,
year = {2018}
}
@article{Chamberland_2018,
doi = {10.1088/2058-9565/aad1f7},
url = {https://doi.org/10.1088%2F2058-9565%2Faad1f7},
year = 2018,
month = {jul},
publisher = {{IOP} Publishing},
volume = {3},
number = {4},
pages = {044002},
author = {Christopher Chamberland and Pooya Ronagh},
title = {Deep neural decoders for near term fault-tolerant experiments},
journal = {Quantum Science and Technology},
abstract = {Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep neural decoders (DND) and apply them to analyze several fault-tolerant error correction (EC) protocols such as the surface code as well as Steane and Knill EC. Our methods require no knowledge of the underlying noise model afflicting the quantum device making them appealing for real-world experiments. Our analysis is based on a full circuit-level noise model. It considers both distance-three and five codes, and is performed near the codes pseudo-threshold regime. Training DND in low noise rate regimes appears to be a challenging machine learning endeavour. We provide a detailed description of our neural network architectures and training methodology. We then discuss both the advantages and limitations of DND. Lastly, we provide a rigorous analysis of the decoding runtime of trained DND and compare our methods with anticipated gate times in future quantum devices. Given the broad applications of our decoding schemes, we believe that the methods presented in this paper could have practical applications for near term fault-tolerant experiments.}
}
@article{Breuckmann2018scalableneural,
doi = {10.22331/q-2018-05-24-68},
url = {https://doi.org/10.22331/q-2018-05-24-68},
title = {Scalable {N}eural {N}etwork {D}ecoders for {H}igher {D}imensional {Q}uantum {C}odes},
author = {Breuckmann, Nikolas P. and Ni, Xiaotong},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {2},
pages = {68},
month = may,
year = {2018}
}
@article{Nautrup2019optimizingquantum,
doi = {10.22331/q-2019-12-16-215},
url = {https://doi.org/10.22331/q-2019-12-16-215},
title = {Optimizing {Q}uantum {E}rror {C}orrection {C}odes with {R}einforcement {L}earning},
author = {Nautrup, Hendrik Poulsen and Delfosse, Nicolas and Dunjko, Vedran and Briegel, Hans J. and Friis, Nicolai},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {3},
pages = {215},
month = dec,
year = {2019}
}
@article{PhysRevLett.122.200501,
title = {Neural Belief-Propagation Decoders for Quantum Error-Correcting Codes},
author = {Liu, Ye-Hua and Poulin, David},
journal = {Phys. Rev. Lett.},
volume = {122},
issue = {20},
pages = {200501},
numpages = {6},
year = {2019},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.122.200501},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.200501}
}
@article{PhysRevA.99.052351,
title = {Advantages of versatile neural-network decoding for topological codes},
author = {Maskara, Nishad and Kubica, Aleksander and Jochym-O'Connor, Tomas},
journal = {Phys. Rev. A},
volume = {99},
issue = {5},
pages = {052351},
numpages = {13},
year = {2019},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.99.052351},
url = {https://link.aps.org/doi/10.1103/PhysRevA.99.052351}
}
@article{Andreasson2019quantumerror,
doi = {10.22331/q-2019-09-02-183},
url = {https://doi.org/10.22331/q-2019-09-02-183},
title = {Quantum error correction for the toric code using deep reinforcement learning},
author = {Andreasson, Philip and Johansson, Joel and Liljestrand, Simon and Granath, Mats},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {3},
pages = {183},
month = sep,
year = {2019}
}
@article{Evert2020QEC,
author={Ryan Sweke and Markus Kesselring and Evert van Nieuwenburg and J. Eisert},
title={Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation},
journal={Machine Learning: Science and Technology},
url={http://iopscience.iop.org/article/10.1088/2632-2153/abc609},
year={2020},
abstract={Topological error correcting codes, and particularly the surface code, currently provide the most feasible road-map towards large-scale fault-tolerant quantum computation. As such, obtaining fast and flexible decoding algorithms for these codes, within the experimentally realistic and challenging context of faulty syndrome measurements, without requiring any final read-out of the physical qubits, is of critical importance. In this work, we show that the problem of decoding such codes can be naturally reformulated as a process of repeated interactions between a decoding agent and a code environment, to which the machinery of reinforcement learning can be applied to obtain decoding agents. While in principle this framework can be instantiated with environments modelling circuit level noise, we take a first step towards this goal by using deepQ learning to obtain decoding agents for a variety of simplified phenomenological noise models, which yield faulty syndrome measurements without including the propagation of errors which arise in full circuit level noise models.}
}
@article{Ni2020neuralnetwork,
doi = {10.22331/q-2020-08-24-310},
url = {https://doi.org/10.22331/q-2020-08-24-310},
title = {Neural {N}etwork {D}ecoders for {L}arge-{D}istance 2{D} {T}oric {C}odes},
author = {Ni, Xiaotong},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {4},
pages = {310},
month = aug,
year = {2020}
}
@article{PhysRevResearch.2.033399,
title = {General framework for constructing fast and near-optimal machine-learning-based decoder of the topological stabilizer codes},
author = {Davaasuren, Amarsanaa and Suzuki, Yasunari and Fujii, Keisuke and Koashi, Masato},
journal = {Phys. Rev. Research},
volume = {2},
issue = {3},
pages = {033399},
numpages = {25},
year = {2020},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.033399},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.033399}
}
@article{PhysRevResearch.2.023230,
title = {Deep Q-learning decoder for depolarizing noise on the toric code},
author = {Fitzek, David and Eliasson, Mattias and Kockum, Anton Frisk and Granath, Mats},
journal = {Phys. Rev. Research},
volume = {2},
issue = {2},
pages = {023230},
numpages = {17},
year = {2020},
month = {May},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.023230},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.023230}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QUANTUM TOMOGRAPHY
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{PhysRevA.55.R1561,
title = {Quantum-state estimation},
author = {Hradil, Z.},
journal = {Phys. Rev. A},
volume = {55},
issue = {3},
pages = {R1561--R1564},
numpages = {0},
year = {1997},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.55.R1561},
url = {https://link.aps.org/doi/10.1103/PhysRevA.55.R1561}
}
@article{PhysRevA.63.040303,
title = {Iterative algorithm for reconstruction of entangled states},
author = {\ifmmode \check{R}\else \v{R}\fi{}eh\'a\ifmmode \check{c}\else \v{c}\fi{}ek, J. and Hradil, Z. and Je\ifmmode \check{z}\else \v{z}\fi{}ek, M.},
journal = {Phys. Rev. A},
volume = {63},
issue = {4},
pages = {040303},
numpages = {4},
year = {2001},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.63.040303},
url = {https://link.aps.org/doi/10.1103/PhysRevA.63.040303}
}
@article{Jezek2003,
author = {Je{\v{z}}ek, Miroslav and Fiur{\'{a}}{\v{s}}ek, Jarom{\'{i}}r and Hradil, Zden{\v{e}}k},
doi = {10.1103/PhysRevA.68.012305},
issn = {1050-2947},
journal = {Physical Review A},
month = {jul},
number = {1},
pages = {012305},
publisher = {American Physical Society},
title = {{Quantum inference of states and processes}},
url = {https://link.aps.org/doi/10.1103/PhysRevA.68.012305},
volume = {68},
year = {2003}
}
@article{PhysRevA.64.052312,
title = {Measurement of qubits},
author = {James, Daniel F. V. and Kwiat, Paul G. and Munro, William J. and White, Andrew G.},
journal = {Phys. Rev. A},
volume = {64},
issue = {5},
pages = {052312},
numpages = {15},
year = {2001},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.64.052312},
url = {https://link.aps.org/doi/10.1103/PhysRevA.64.052312}
}
@article{Banaszek2013,
author = {Banaszek, K and Cramer, M and Gross, D},
doi = {10.1088/1367-2630/15/12/125020},
issn = {1367-2630},
journal = {New Journal of Physics},
month = {dec},
number = {12},
pages = {125020},
title = {{Focus on quantum tomography}},
url = {http://stacks.iop.org/1367-2630/15/i=12/a=125020?key=crossref.d640bfdf036841021cae0e5aafd08554},
volume = {15},
year = {2013}
}
@article{vogel89,
title = {Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase},
author = {Vogel, K. and Risken, H.},
journal = {Phys. Rev. A},
volume = {40},
issue = {5},
pages = {2847--2849},
numpages = {0},
year = {1989},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.40.2847},
url = {https://link.aps.org/doi/10.1103/PhysRevA.40.2847}
}
@article{PhysRevLett.105.150401,
title = {Quantum State Tomography via Compressed Sensing},
author = {Gross, David and Liu, Yi-Kai and Flammia, Steven T. and Becker, Stephen and Eisert, Jens},
journal = {Phys. Rev. Lett.},
volume = {105},
issue = {15},
pages = {150401},
numpages = {4},
year = {2010},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.105.150401},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.105.150401}
}
@article{Flammia_2012,
doi = {10.1088/1367-2630/14/9/095022},
url = {https://doi.org/10.1088%2F1367-2630%2F14%2F9%2F095022},
year = 2012,
month = {sep},
publisher = {{IOP} Publishing},
volume = {14},
number = {9},
pages = {095022},
author = {Steven T Flammia and David Gross and Yi-Kai Liu and Jens Eisert},
title = {Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators},
journal = {New Journal of Physics},
abstract = {Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. Firstly, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e. the sample complexity of tomography decreases with the rank. Secondly, we show that unknown low-rank states can be reconstructed from an incomplete set of measurements, using techniques from compressed sensing and matrix completion. These techniques use simple Pauli measurements, and their output can be certified without making any assumptions about the unknown state. In this paper, we present a new theoretical analysis of compressed tomography, based on the restricted isometry property for low-rank matrices. Using these tools, we obtain near-optimal error bounds for the realistic situation where the data contain noise due to finite statistics, and the density matrix is full-rank with decaying eigenvalues. We also obtain upper bounds on the sample complexity of compressed tomography, and almost-matching lower bounds on the sample complexity of any procedure using adaptive sequences of Pauli measurements. Using numerical simulations, we compare the performance of two compressed sensing estimators—the matrix Dantzig selector and the matrix Lasso—with standard maximum-likelihood estimation (MLE). We find that, given comparable experimental resources, the compressed sensing estimators consistently produce higher fidelity state reconstructions than MLE. In addition, the use of an incomplete set of measurements leads to faster classical processing with no loss of accuracy. Finally, we show how to certify the accuracy of a low-rank estimate using direct fidelity estimation, and describe a method for compressed quantum process tomography that works for processes with small Kraus rank and requires only Pauli eigenstate preparations and Pauli measurements.}
}
@article{riofrio_experimental_2017,
title = {Experimental quantum compressed sensing for a seven-qubit system},
volume = {8},
issn = {2041-1723},
url = {https://doi.org/10.1038/ncomms15305},
doi = {10.1038/ncomms15305},
abstract = {Well-controlled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: state-of-the-art systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a seven-qubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few non-zero eigenvalues. We argue that low-rank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a random-matrix model that carries no information about the true state.},
number = {1},
journal = {Nature Communications},
author = {Riofrío, C. A. and Gross, D. and Flammia, S. T. and Monz, T. and Nigg, D. and Blatt, R. and Eisert, J.},
month = may,
year = {2017},
pages = {15305},
}
@article{Blume_Kohout_2010,
doi = {10.1088/1367-2630/12/4/043034},
url = {https://doi.org/10.1088%2F1367-2630%2F12%2F4%2F043034},
year = 2010,
month = {apr},
publisher = {{IOP} Publishing},
volume = {12},
number = {4},
pages = {043034},
author = {Robin Blume-Kohout},
title = {Optimal, reliable estimation of quantum states},
journal = {New Journal of Physics},
abstract = {Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE), generally reports an estimate with zero eigenvalues. These cannot be justified. Furthermore, the MLE estimate is incompatible with error bars, so conclusions drawn from it are suspect. I propose an alternative procedure, Bayesian mean estimation (BME). BME never yields zero eigenvalues, its eigenvalues provide a bound on their own uncertainties, and under certain circumstances it is provably the most accurate procedure possible. I show how to implement BME numerically, and how to obtain natural error bars that are compatible with the estimate. Finally, I briefly discuss the differences between Bayesian and frequentist estimation techniques.}
}
@article{Granade_2017,
doi = {10.1088/1367-2630/aa8fe6},
url = {https://doi.org/10.1088%2F1367-2630%2Faa8fe6},
year = 2017,
month = {nov},
publisher = {{IOP} Publishing},
volume = {19},
number = {11},
pages = {113017},
author = {Christopher Granade and Christopher Ferrie and Steven T Flammia},
title = {Practical adaptive quantum tomography},
journal = {New Journal of Physics},
abstract = {We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.}
}
@article{PhysRevLett.108.070502,
title = {Efficient Method for Computing the Maximum-Likelihood Quantum State from Measurements with Additive Gaussian Noise},
author = {Smolin, John A. and Gambetta, Jay M. and Smith, Graeme},
journal = {Phys. Rev. Lett.},
volume = {108},
issue = {7},
pages = {070502},
numpages = {4},
year = {2012},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.108.070502},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.070502}
}
@article{PhysRevLett.106.100401,
title = {Efficient Measurement of Quantum Dynamics via Compressive Sensing},
author = {Shabani, A. and Kosut, R. L. and Mohseni, M. and Rabitz, H. and Broome, M. A. and Almeida, M. P. and Fedrizzi, A. and White, A. G.},
journal = {Phys. Rev. Lett.},
volume = {106},
issue = {10},
pages = {100401},
numpages = {4},
year = {2011},
month = {Mar},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.106.100401},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.106.100401}
}
@article{cramer2009efficient,
Author = {Cramer, M and Plenio, MB and Flammia, ST and Somma, R and Gross, D and Bartlett, SD and Landon-Cardinal, O and Poulin, D and Liu, YK},
Date-Added = {2020-05-19 19:53:36 +0000},
Date-Modified = {2020-05-19 19:53:36 +0000},
Journal = {Nature communications},
Pages = {149},
Title = {Efficient quantum state tomography.},
Url = {http://www.nature.com/articles/ncomms1147},
Volume = {1},
Year = {2009},
Bdsk-Url-1 = {http://www.nature.com/articles/ncomms1147}}
@article{MPOtomo,
Author = {Baumgratz, T. and Gross, D. and Cramer, M. and Plenio, M. B.},
Doi = {10.1103/PhysRevLett.111.020401},
Issue = {2},
Journal = {Phys. Rev. Lett.},
Month = {Jul},
Numpages = {5},
Pages = {020401},
Publisher = {American Physical Society},
Title = {Scalable Reconstruction of Density Matrices},
Url = {https://link.aps.org/doi/10.1103/PhysRevLett.111.020401},
Volume = {111},
Year = {2013},
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.111.020401},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.111.020401}}
@article{LeiWang2020,
Author = {Wang, Jun and Han, Zhao-Yu and Wang, Song-Bo and Li, Zeyang and Mu, Liang-Zhu and Fan, Heng and Wang, Lei},
Doi = {10.1103/PhysRevA.101.032321},
Issue = {3},
Journal = {Phys. Rev. A},
Month = {Mar},
Numpages = {11},
Pages = {032321},
Publisher = {American Physical Society},
Title = {Scalable quantum tomography with fidelity estimation},
Url = {https://link.aps.org/doi/10.1103/PhysRevA.101.032321},
Volume = {101},
Year = {2020},
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevA.101.032321},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevA.101.032321}}
@article{huang_predicting_2020,
title = {Predicting many properties of a quantum system from very few measurements},
volume = {16},
issn = {1745-2481},
url = {https://doi.org/10.1038/s41567-020-0932-7},
doi = {10.1038/s41567-020-0932-7},
abstract = {Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order \$\$\{{\textbackslash}mathrm\{log\}\}{\textbackslash},(M)\$\$log(M)measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.},
number = {10},
journal = {Nature Physics},
author = {Huang, Hsin-Yuan and Kueng, Richard and Preskill, John},
month = oct,
year = {2020},
pages = {1050--1057},
}
@article{Lanyon2017,
Abstract = {Traditionally quantum state tomography is used to characterize a quantum state, but it becomes exponentially hard with the system size. An alternative technique, matrix product state tomography, is shown to work well in practical situations.},
Author = {Lanyon, B. P. and Maier, C. and Holz{\"{a}}pfel, M. and Baumgratz, T. and Hempel, C. and Jurcevic, P. and Dhand, I. and Buyskikh, A. S. and Daley, A. J. and Cramer, M. and Plenio, M. B. and Blatt, R. and Roos, C. F.},
Doi = {10.1038/nphys4244},
File = {:Users/btimar/Library/Application Support/Mendeley Desktop/Downloaded/Lanyon et al. - 2017 - Efficient tomography of a quantum many-body system.pdf:pdf},
Issn = {1745-2473},
Journal = {Nature Physics},
Keywords = {Quantum information,Quantum simulation},
Month = {sep},
Number = {12},
Pages = {1158--1162},
Publisher = {Nature Publishing Group},
Title = {{Efficient tomography of a quantum many-body system}},
Url = {http://www.nature.com/doifinder/10.1038/nphys4244},
Volume = {13},
Year = {2017},
Bdsk-Url-1 = {http://www.nature.com/doifinder/10.1038/nphys4244},
Bdsk-Url-2 = {https://doi.org/10.1038/nphys4244}}
@article{eisert_quantum_2020,
title = {Quantum certification and benchmarking},
volume = {2},
issn = {2522-5820},
url = {https://doi.org/10.1038/s42254-020-0186-4},
doi = {10.1038/s42254-020-0186-4},
abstract = {With the rapid development of quantum technologies, a pressing need has emerged for a wide array of tools for the certification and characterization of quantum devices. Such tools are critical because the powerful applications of quantum information science will only be realized if stringent levels of precision of components can be reached and their functioning guaranteed. This Technical Review provides a brief overview of the known characterization methods for certification, benchmarking and tomographic reconstruction of quantum states and processes, and outlines their applications in quantum computing, simulation and communication.},
number = {7},
journal = {Nature Reviews Physics},
author = {Eisert, Jens and Hangleiter, Dominik and Walk, Nathan and Roth, Ingo and Markham, Damian and Parekh, Rhea and Chabaud, Ulysse and Kashefi, Elham},
month = jul,
year = {2020},
pages = {382--390},
}
@misc{pastaq,
title={\mbox{PastaQ}: A Package for Simulation, Tomography and Analysis of Quantum Computers},
author={Matthew Fishman and Giacomo Torlai},
year={2020},
url={https://github.com/GTorlai/PastaQ.jl/}
}
@ARTICLE{qucumber,
author = {{Beach}, Matthew J.~S. and {De Vlugt}, Isaac and {Golubeva}, Anna and
{Huembeli}, Patrick and {Kulchytskyy}, Bohdan and {Luo}, Xiuzhe and
{Melko}, Roger G. and {Merali}, Ejaaz and {Torlai}, Giacomo},
title = "{QuCumber: wavefunction reconstruction with neural networks}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Strongly Correlated Electrons},
year = "2018",
month = "Dec",
eid = {arXiv:1812.09329},
pages = {arXiv:1812.09329},
archivePrefix = {arXiv},
eprint = {1812.09329},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/\#abs/2018arXiv181209329B},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevB.85.165146,
title = {Perfect sampling with unitary tensor networks},
author = {Ferris, Andrew J. and Vidal, Guifre},
journal = {Phys. Rev. B},
volume = {85},
issue = {16},
pages = {165146},
numpages = {10},
year = {2012},
month = {Apr},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.85.165146},
url = {https://link.aps.org/doi/10.1103/PhysRevB.85.165146}
}
@ARTICLE{netket,
author = {{Carleo}, Giuseppe and {Choo}, Kenny and {Hofmann}, Damian and
{Smith}, James E.~T. and {Westerhout}, Tom and {Alet}, Fabien and
{Davis}, Emily J. and {Efthymiou}, Stavros and {Glasser}, Ivan and
{Lin}, Sheng-Hsuan and {Mauri}, Marta and {Mazzola}, Guglielmo and
{Mendl}, Christian B. and {van Nieuwenburg}, Evert and
{O'Reilly}, Ossian and {Th{\'e}veniaut}, Hugo and {Torlai}, Giacomo and
{Wietek}, Alexander},
title = "{NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Strongly Correlated Electrons, Physics - Computational Physics, Physics - Data Analysis, Statistics and Probability},
year = "2019",
month = "Mar",
eid = {arXiv:1904.00031},
pages = {arXiv:1904.00031},
archivePrefix = {arXiv},
eprint = {1904.00031},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190400031C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{torlai_learning_2016,
Abstract = {A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modeling thermodynamic observables for physical systems in thermal equilibrium. Through unsupervised learning, we train the Boltzmann machine on data sets constructed with spin configurations importance sampled from the partition function of an Ising Hamiltonian at different temperatures using Monte Carlo (MC) methods. The trained Boltzmann machine is then used to generate spin states, for which we compare thermodynamic observables to those computed by direct MC sampling. We demonstrate that the Boltzmann machine can faithfully reproduce the observables of the physical system. Further, we observe that the number of neurons required to obtain accurate results increases as the system is brought close to criticality.},
Author = {Torlai, Giacomo and Melko, Roger G.},
Doi = {10.1103/PhysRevB.94.165134},
Journal = {Physical Review B},
Month = oct,
Number = {16},
Pages = {165134},
Title = {Learning thermodynamics with {Boltzmann} machines},
Url = {http://link.aps.org/doi/10.1103/PhysRevB.94.165134},
Urldate = {2017-01-20},
Volume = {94},
Year = {2016},
Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevB.94.165134},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevB.94.165134}}
@article{torlai_Tomo,
Author = {Torlai, Giacomo and Mazzola, Guglielmo and Carrasquilla, Juan and Troyer, Matthias and Melko, Roger and Carleo, Giuseppe},
Doi = {10.1038/s41567-018-0048-5},
Journal = {Nature Physics},
Number = {5},
Pages = {447--450},
Title = {Neural-network quantum state tomography},
Url = {https://doi.org/10.1038/s41567-018-0048-5},
Volume = {14},
Year = {2018}
}
@article{rocchetto,
Abstract = {The exact description of many-body quantum systems represents one of the major challenges in modern physics, because it requires an amount of computational resources that scales exponentially with the size of the system. Simulating the evolution of a state, or even storing its description, rapidly becomes intractable for exact classical algorithms. Recently, machine learning techniques, in the form of restricted Boltzmann machines, have been proposed as a way to efficiently represent certain quantum states with applications in state tomography and ground state estimation. Here, we introduce a practically usable deep architecture for representing and sampling from probability distributions of quantum states. Our representation is based on variational auto-encoders, a type of generative model in the form of a neural network. We show that this model is able to learn efficient representations of states that are easy to simulate classically and can compress states that are not classically tractable. Specifically, we consider the learnability of a class of quantum states introduced by Fefferman and Umans. Such states are provably hard to sample for classical computers, but not for quantum ones, under plausible computational complexity assumptions. The good level of compression achieved for hard states suggests these methods can be suitable for characterizing states of the size expected in first generation quantum hardware.},
Author = {Rocchetto, Andrea and Grant, Edward and Strelchuk, Sergii and Carleo, Giuseppe and Severini, Simone},
Da = {2018/06/28},
Date-Added = {2019-03-27 20:12:35 +0000},
Date-Modified = {2019-03-27 20:12:35 +0000},
Doi = {10.1038/s41534-018-0077-z},
Id = {Rocchetto2018},
Isbn = {2056-6387},
Journal = {npj Quantum Information},
Number = {1},
Pages = {28},
Title = {Learning hard quantum distributions with variational autoencoders},
Ty = {JOUR},
Url = {https://doi.org/10.1038/s41534-018-0077-z},
Volume = {4},
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1038/s41534-018-0077-z}}
@article{Torlai_latent,
title = {Latent Space Purification via Neural Density Operators},
author = {Torlai, Giacomo and Melko, Roger G.},
journal = {Phys. Rev. Lett.},
volume = {120},
issue = {24},
pages = {240503},
numpages = {5},
year = {2018},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.120.240503},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.240503}
}
@ARTICLE{2018arXiv181206693Q,
author = {{Quek}, Yihui and {Fort}, Stanislav and {Khoon Ng}, Hui},
title = "{Adaptive Quantum State Tomography with Neural Networks}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Computer Science - Machine Learning},
year = 2018,
month = dec,
eid = {arXiv:1812.06693},
pages = {arXiv:1812.06693},
archivePrefix = {arXiv},
eprint = {1812.06693},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2018arXiv181206693Q},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{carrasquilla_povm,
Abstract = {A major bottleneck in the development of scalable many-body quantum technologies is the difficulty in benchmarking state preparations, which suffer from an exponential `curse of dimensionality'inherent to the classical description of quantum states. We present an experimentally friendly method for density matrix reconstruction based on neural network generative models. The learning procedure comes with a built-in approximate certificate of the reconstruction and makes no assumptions about the purity of the state under scrutiny. It can efficiently handle a broad class of complex systems including prototypical states in quantum information, as well as ground states of local spin models common to condensed matter physics. The key insight is to reduce state tomography to an unsupervised learning problem of the statistics of an informationally complete quantum measurement. This constitutes a modern machine learning approach to the validation of complex quantum devices, which may in addition prove relevant as a neural-network ansatz over mixed states suitable for variational optimization.},
Author = {Carrasquilla, Juan and Torlai, Giacomo and Melko, Roger G. and Aolita, Leandro},
Da = {2019/03/01},
Date-Added = {2019-03-28 12:52:13 +0000},
Date-Modified = {2019-03-28 12:52:13 +0000},
Doi = {10.1038/s42256-019-0028-1},
Id = {Carrasquilla2019},
Isbn = {2522-5839},
Journal = {Nature Machine Intelligence},
Number = {3},
Pages = {155--161},
Title = {Reconstructing quantum states with generative models},
Ty = {JOUR},
Url = {https://doi.org/10.1038/s42256-019-0028-1},
Volume = {1},
Year = {2019},
Bdsk-Url-1 = {https://doi.org/10.1038/s42256-019-0028-1}}
@article{biamonte_qst,
title = {Experimental neural network enhanced quantum tomography},
volume = {6},
issn = {2056-6387},
url = {https://doi.org/10.1038/s41534-020-0248-6},
doi = {10.1038/s41534-020-0248-6},
abstract = {Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state-preparation-and-measurement (SPAM) apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to SPAM errors degrading reconstruction performance. Here we develop a framework based on machine learning which generally applies to both the tomography and SPAM mitigation problem. We experimentally implement our method. We trained a supervised neural network to filter the experimental data and hence uncovered salient patterns that characterize the measurement probabilities for the original state and the ideal experimental apparatus free from SPAM errors. We compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography, as well as to an SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity is shown to be enhanced by 10\% and 27\%, respectively. The presented methods apply to the vast range of quantum experiments which rely on tomography.},
number = {1},
journal = {npj Quantum Information},
author = {Palmieri, Adriano Macarone and Kovlakov, Egor and Bianchi, Federico and Yudin, Dmitry and Straupe, Stanislav and Biamonte, Jacob D. and Kulik, Sergei},
month = feb,
year = {2020},
pages = {20},
}
@ARTICLE{torlai19,
author = {{Torlai}, Giacomo and {Timar}, Brian and {van Nieuwenburg}, Evert P.~L. and
{Levine}, Harry and {Omran}, Ahmed and {Keesling}, Alexander and
{Bernien}, Hannes and {Greiner}, Markus and {Vuleti{\'c}}, Vladan and
{Lukin}, Mikhail D. and {Melko}, Roger G. and {Endres}, Manuel},
title = "{Integrating Neural Networks with a Quantum Simulator for State Reconstruction}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Quantum Gases},
year = "2019",
month = "Apr",
eid = {arXiv:1904.08441},
pages = {arXiv:1904.08441},
archivePrefix = {arXiv},
eprint = {1904.08441},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2019arXiv190408441T},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{torlai_rydberg19,
title = {Integrating Neural Networks with a Quantum Simulator for State Reconstruction},
author = {Torlai, Giacomo and Timar, Brian and van Nieuwenburg, Evert P. L. and Levine, Harry and Omran, Ahmed and Keesling, Alexander and Bernien, Hannes and Greiner, Markus and Vuleti\ifmmode \acute{c}\else \'{c}\fi{}, Vladan and Lukin, Mikhail D. and Melko, Roger G. and Endres, Manuel},
journal = {Phys. Rev. Lett.},
volume = {123},
issue = {23},
pages = {230504},
numpages = {6},
year = {2019},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.123.230504},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.230504}
}
@article{xin_local-measurement-based_2019,
title = {Local-measurement-based quantum state tomography via neural networks},
volume = {5},
issn = {2056-6387},
url = {https://doi.org/10.1038/s41534-019-0222-3},
doi = {10.1038/s41534-019-0222-3},
abstract = {Quantum state tomography is a daunting challenge of experimental quantum computing, even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine-learning method to recover the ground states of \$\$k\$\$k-local Hamiltonians from just the local information, where a fully connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems.},
number = {1},
journal = {npj Quantum Information},
author = {Xin, Tao and Lu, Sirui and Cao, Ningping and Anikeeva, Galit and Lu, Dawei and Li, Jun and Long, Guilu and Zeng, Bei},
month = nov,
year = {2019},
pages = {109},
}
@article{Sehayek2019,
title = {Learnability scaling of quantum states: Restricted Boltzmann machines},
author = {Sehayek, Dan and Golubeva, Anna and Albergo, Michael S. and Kulchytskyy, Bohdan and Torlai, Giacomo and Melko, Roger G.},
journal = {Phys. Rev. B},
volume = {100},
issue = {19},
pages = {195125},
numpages = {7},
year = {2019},
month = {Nov},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.100.195125},
url = {https://link.aps.org/doi/10.1103/PhysRevB.100.195125}
}
@article{torlai_chemistry,
title = {Precise measurement of quantum observables with neural-network estimators},
author = {Torlai, Giacomo and Mazzola, Guglielmo and Carleo, Giuseppe and Mezzacapo, Antonio},
journal = {Phys. Rev. Research},
volume = {2},
issue = {2},
pages = {022060},
numpages = {6},
year = {2020},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.022060},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.022060}
}
@article{PhysRevA.102.022412,
title = {Eigenstate extraction with neural-network tomography},
author = {Melkani, Abhijeet and Gneiting, Clemens and Nori, Franco},
journal = {Phys. Rev. A},
volume = {102},
issue = {2},
pages = {022412},
numpages = {11},
year = {2020},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.102.022412},
url = {https://link.aps.org/doi/10.1103/PhysRevA.102.022412}
}
@ARTICLE{NoriGAN,
author = {{Ahmed}, Shahnawaz and {S{\'a}nchez Mu{\~n}oz}, Carlos and {Nori}, Franco and {Frisk Kockum}, Anton},
title = "{Quantum State Tomography with Conditional Generative Adversarial Networks}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Computer Science - Machine Learning},
year = 2020,
month = aug,
eid = {arXiv:2008.03240},
pages = {arXiv:2008.03240},
archivePrefix = {arXiv},
eprint = {2008.03240},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200803240A},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{Tiunov:20,
author = {E. S. Tiunov and V. V. Tiunova (Vyborova) and A. E. Ulanov and A. I. Lvovsky and A. K. Fedorov},
journal = {Optica},
keywords = {Atomic ensembles; Condensed matter; Neural networks; Optomechanics; Parametric oscillators; Quantum information processing},
number = {5},
pages = {448--454},
publisher = {OSA},
title = {Experimental quantum homodyne tomography via machine learning},
volume = {7},
month = {May},
year = {2020},
url = {http://www.osapublishing.org/optica/abstract.cfm?URI=optica-7-5-448},
doi = {10.1364/OPTICA.389482},
abstract = {Complete characterization of states and processes that occur within quantum devices is crucial for understanding and testing their potential to outperform classical technologies for communications and computing. However, solving this task with current state-of-the-art techniques becomes unwieldy for large and complex quantum systems. Here we realize and experimentally demonstrate a method for complete characterization of a quantum harmonic oscillator based on an artificial neural network known as the restricted Boltzmann machine. We apply the method to optical homodyne tomography and show it to allow full estimation of quantum states based on a smaller amount of experimental data compared to state-of-the-art methods. We link this advantage to reduced overfitting. Although our experiment is in the optical domain, our method provides a way of exploring quantum resources in a broad class of large-scale physical systems, such as superconducting circuits, atomic and molecular ensembles, and optomechanical systems.},
}
@ARTICLE{Cha2020,
author = {{Cha}, Peter and {Ginsparg}, Paul and {Wu}, Felix and {Carrasquilla}, Juan and {McMahon}, Peter L. and {Kim}, Eun-Ah},
title = "{Attention-based Quantum Tomography}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Computer Science - Machine Learning},
year = 2020,
month = jun,
eid = {arXiv:2006.12469},
pages = {arXiv:2006.12469},
archivePrefix = {arXiv},
eprint = {2006.12469},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200612469C},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevA.102.042604,
title = {Neural-network quantum state tomography in a two-qubit experiment},
author = {Neugebauer, Marcel and Fischer, Laurin and J\"ager, Alexander and Czischek, Stefanie and Jochim, Selim and Weidem\"uller, Matthias and G\"arttner, Martin},
journal = {Phys. Rev. A},
volume = {102},
issue = {4},
pages = {042604},
numpages = {7},
year = {2020},
month = {Oct},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.102.042604},
url = {https://link.aps.org/doi/10.1103/PhysRevA.102.042604}
}
@article{DeVlugt2020,
title = {Reconstructing quantum molecular rotor ground states},
author = {De Vlugt, Isaac J. S. and Iouchtchenko, Dmitri and Merali, Ejaaz and Roy, Pierre-Nicholas and Melko, Roger G.},
journal = {Phys. Rev. B},
volume = {102},
issue = {3},
pages = {035108},
numpages = {10},
year = {2020},
month = {Jul},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.102.035108},
url = {https://link.aps.org/doi/10.1103/PhysRevB.102.035108}
}
@ARTICLE{2020arXiv200907601S,
author = {{Smith}, Alistair W.~R. and {Gray}, Johnnie and {Kim}, M.~S.},
title = "{Efficient Approximate Quantum State Tomography with Basis Dependent Neural-Networks}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Computer Science - Machine Learning},
year = 2020,
month = sep,
eid = {arXiv:2009.07601},
pages = {arXiv:2009.07601},
archivePrefix = {arXiv},
eprint = {2009.07601},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200907601S},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@ARTICLE{torlai_QPT,
author = {{Torlai}, Giacomo and {Wood}, Christopher J. and {Acharya}, Atithi and {Carleo}, Giuseppe and {Carrasquilla}, Juan and {Aolita}, Leandro},
title = "{Quantum process tomography with unsupervised learning and tensor networks}",
journal = {arXiv e-prints},
keywords = {Quantum Physics},
year = 2020,
month = jun,
eid = {arXiv:2006.02424},
pages = {arXiv:2006.02424},
archivePrefix = {arXiv},
eprint = {2006.02424},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv200602424T},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@article{PhysRevE.96.022140,
title = {Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders},
author = {Wetzel, Sebastian J.},
journal = {Phys. Rev. E},
volume = {96},
issue = {2},
pages = {022140},
numpages = {11},
year = {2017},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevE.96.022140},
url = {https://link.aps.org/doi/10.1103/PhysRevE.96.022140}
}
@ARTICLE{morawetz2020,
author = {{Morawetz}, Stewart and {De Vlugt}, Isaac J.~S. and {Carrasquilla}, Juan and {Melko}, Roger G.},
title = "{U(1) symmetric recurrent neural networks for quantum state reconstruction}",
journal = {arXiv e-prints},
keywords = {Quantum Physics, Condensed Matter - Strongly Correlated Electrons},
year = 2020,
month = oct,
eid = {arXiv:2010.14514},
pages = {arXiv:2010.14514},
archivePrefix = {arXiv},
eprint = {2010.14514},
primaryClass = {quant-ph},
adsurl = {https://ui.adsabs.harvard.edu/abs/2020arXiv201014514M},
adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
@misc{Nori2020,
title={Classification and reconstruction of optical quantum states with deep neural networks},
author={Shahnawaz Ahmed and Carlos Sánchez Munoz and Franco Nori and Anton Frisk Kockum},
year={2020},
eprint={2012.02185},
archivePrefix={arXiv},
primaryClass={quant-ph}
}
%%%%
%DFT
%%%
@article{PhysRevLett.108.253002,
title = {Finding Density Functionals with Machine Learning},
author = {Snyder, John C. and Rupp, Matthias and Hansen, Katja and M\"uller, Klaus-Robert and Burke, Kieron},
journal = {Phys. Rev. Lett.},
volume = {108},
issue = {25},
pages = {253002},
numpages = {5},
year = {2012},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.108.253002},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.108.253002}
}
@article{doi:10.1063/1.4834075,
author = {Snyder,John C. and Rupp,Matthias and Hansen,Katja and Blooston,Leo and Müller,Klaus-Robert and Burke,Kieron },
title = {Orbital-free bond breaking via machine learning},
journal = {The Journal of Chemical Physics},
volume = {139},
number = {22},
pages = {224104},
year = {2013},
doi = {10.1063/1.4834075},
URL = {
https://doi.org/10.1063/1.4834075
},
eprint = {
https://doi.org/10.1063/1.4834075
}
}
@article{silver2016,
title = {Mastering the Game of {{Go}} with Deep Neural Networks and Tree Search},
author = {Silver, David and Huang, Aja and Maddison, Chris J. and Guez, Arthur and Sifre, Laurent and {van den Driessche}, George and Schrittwieser, Julian and Antonoglou, Ioannis and Panneershelvam, Veda and Lanctot, Marc and Dieleman, Sander and Grewe, Dominik and Nham, John and Kalchbrenner, Nal and Sutskever, Ilya and Lillicrap, Timothy and Leach, Madeleine and Kavukcuoglu, Koray and Graepel, Thore and Hassabis, Demis},
year = {2016},
month = jan,
volume = {529},
pages = {484--489},
publisher = {{Nature Publishing Group}},
issn = {1476-4687},
doi = {10.1038/nature16961},
abstract = {The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses `value networks' to evaluate board positions and `policy networks' to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of state-of-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8\% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away.},
journal = {Nature},
number = {7587}
}
@article{PhysRevB.94.245129,
title = {Pure density functional for strong correlation and the thermodynamic limit from machine learning},
author = {Li, Li and Baker, Thomas E. and White, Steven R. and Burke, Kieron},
journal = {Phys. Rev. B},
volume = {94},
issue = {24},
pages = {245129},
numpages = {9},
year = {2016},
month = {Dec},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.94.245129},
url = {https://link.aps.org/doi/10.1103/PhysRevB.94.245129}
}
@article{rao2018,
title = {Machine Learning the Many-Body Localization Transition in Random Spin Systems},
author = {Rao, Wen-Jia},
year = {2018},
month = sep,
volume = {30},
pages = {395902},
publisher = {{IOP Publishing}},
issn = {0953-8984},
doi = {10.1088/1361-648X/aaddc6},
abstract = {The transition between thermal and many-body localized phases in isolated random spin systems are typically identified by the distribution of nearest level spacings. In this work, by employing machine learning methodology, we show this transition can be learnt through raw energy spectrum without any pre-processing. After achieving so in conventional random spin chain with differentiable level spacing distributions, we further construct novel models with misleading signatures of level spacing, and show machine can defeat the latter when training data is raw energy spectrum. Our work shows the low-level energy spectrum contains more information than level spacings, and can be captured by machine in a direct while efficient way, which makes it a promising new tool for studying a variety of isolated quantum systems.},
journal = {Journal of Physics: Condensed Matter},
number = {39}
}
@article{PhysRevLett.120.257204,
title = {Machine Learning Out-of-Equilibrium Phases of Matter},
author = {Venderley, Jordan and Khemani, Vedika and Kim, Eun-Ah},
journal = {Phys. Rev. Lett.},
volume = {120},
issue = {25},
pages = {257204},
numpages = {6},
year = {2018},
month = {Jun},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.120.257204},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.120.257204}
}
@article{brockherde_bypassing_2017,
title = {Bypassing the {Kohn}-{Sham} equations with machine learning},
volume = {8},
issn = {2041-1723},
url = {https://doi.org/10.1038/s41467-017-00839-3},
doi = {10.1038/s41467-017-00839-3},
abstract = {Last year, at least 30,000 scientific papers used the Kohn–Sham scheme of density functional theory to solve electronic structure problems in a wide variety of scientific fields. Machine learning holds the promise of learning the energy functional via examples, bypassing the need to solve the Kohn–Sham equations. This should yield substantial savings in computer time, allowing larger systems and/or longer time-scales to be tackled, but attempts to machine-learn this functional have been limited by the need to find its derivative. The present work overcomes this difficulty by directly learning the density-potential and energy-density maps for test systems and various molecules. We perform the first molecular dynamics simulation with a machine-learned density functional on malonaldehyde and are able to capture the intramolecular proton transfer process. Learning density models now allows the construction of accurate density functionals for realistic molecular systems.},
number = {1},
journal = {Nature Communications},
author = {Brockherde, Felix and Vogt, Leslie and Li, Li and Tuckerman, Mark E. and Burke, Kieron and Müller, Klaus-Robert},
month = oct,
year = {2017},
pages = {872},
}
@article{Seif_2018,
doi = {10.1088/1361-6455/aad62b},
url = {https://doi.org/10.1088%2F1361-6455%2Faad62b},
year = 2018,
month = {aug},
publisher = {{IOP} Publishing},
volume = {51},
number = {17},
pages = {174006},
author = {Alireza Seif and Kevin A Landsman and Norbert M Linke and Caroline Figgatt and C Monroe and Mohammad Hafezi},
title = {Machine learning assisted readout of trapped-ion qubits},
journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
abstract = {We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30 improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.}
}
@article{PhysRevB.99.075113,
title = {Super-resolving the Ising model with convolutional neural networks},
author = {Efthymiou, Stavros and Beach, Matthew J. S. and Melko, Roger G.},
journal = {Phys. Rev. B},
volume = {99},
issue = {7},
pages = {075113},
numpages = {9},
year = {2019},
month = {Feb},
publisher = {American Physical Society},
doi = {10.1103/PhysRevB.99.075113},
url = {https://link.aps.org/doi/10.1103/PhysRevB.99.075113}
}
@article{PhysRevA.100.022512,
title = {Deep learning and density-functional theory},
author = {Ryczko, Kevin and Strubbe, David A. and Tamblyn, Isaac},
journal = {Phys. Rev. A},
volume = {100},
issue = {2},
pages = {022512},
numpages = {11},
year = {2019},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevA.100.022512},
url = {https://link.aps.org/doi/10.1103/PhysRevA.100.022512}
}
@article{PhysRevLett.125.076402,
title = {Deep Learning the Hohenberg-Kohn Maps of Density Functional Theory},
author = {Moreno, Javier Robledo and Carleo, Giuseppe and Georges, Antoine},
journal = {Phys. Rev. Lett.},
volume = {125},
issue = {7},
pages = {076402},
numpages = {6},
year = {2020},
month = {Aug},
publisher = {American Physical Society},
doi = {10.1103/PhysRevLett.125.076402},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.125.076402}
}
@article{PhysRevResearch.2.033388,
title = {Efficient learning of a one-dimensional density functional theory},
author = {Denner, M. Michael and Fischer, Mark H. and Neupert, Titus},
journal = {Phys. Rev. Research},
volume = {2},
issue = {3},
pages = {033388},
numpages = {9},
year = {2020},
month = {Sep},
publisher = {American Physical Society},
doi = {10.1103/PhysRevResearch.2.033388},
url = {https://link.aps.org/doi/10.1103/PhysRevResearch.2.033388}
}
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