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  {\bibinfo {title} {{Identifying Quantum Phase Transitions using Artificial
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\bibitem [{\citenamefont {Lian}\ \emph {et~al.}(2019)\citenamefont {Lian},
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  \citenamefont {Ouyang}, \citenamefont {Wang}, \citenamefont {Huang},
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  \bibinfo {author} {\bibfnamefont {Li}~\bibnamefont {He}}, \bibinfo {author}
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  {\bibfnamefont {Dong-Ling}\ \bibnamefont {Deng}}, \ and\ \bibinfo {author}
  {\bibfnamefont {Luming}\ \bibnamefont {Duan}},\ }\bibfield  {title} {\enquote
  {\bibinfo {title} {Machine learning topological phases with a solid-state
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\bibitem [{\citenamefont {Liu}\ \emph {et~al.}(2017)\citenamefont {Liu},
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  {McNaughton}, \citenamefont {Milo\ifmmode \check{s}\else
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  \BibitemOpen
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  \BibitemOpen
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\bibitem [{\citenamefont {Androsiuk}\ \emph {et~al.}(1993)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {{Lagaris}}\ \emph {et~al.}(1998)\citenamefont
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  \BibitemOpen
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  {Troyer}(2017)}]{Carleo_2017}%
  \BibitemOpen
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\bibitem [{\citenamefont {Coopmans}\ \emph {et~al.}(2020)\citenamefont
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\bibitem [{\citenamefont {Torlai}\ \emph {et~al.}(2018)\citenamefont {Torlai},
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\bibitem [{\citenamefont {Rocchetto}\ \emph {et~al.}(2018)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {Torlai}\ and\ \citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {{Quek}}\ \emph {et~al.}(2018)\citenamefont {{Quek}},
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  \BibitemOpen
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\bibitem [{\citenamefont {Carrasquilla}\ \emph {et~al.}(2019)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {Palmieri}\ \emph {et~al.}(2020)\citenamefont
  {Palmieri}, \citenamefont {Kovlakov}, \citenamefont {Bianchi}, \citenamefont
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\bibitem [{\citenamefont {Torlai}\ \emph {et~al.}(2019)\citenamefont {Torlai},
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  {Bernien}, \citenamefont {Greiner}, \citenamefont
  {Vuleti\ifmmode~\acute{c}\else \'{c}\fi{}}, \citenamefont {Lukin},
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  \BibitemOpen
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\bibitem [{\citenamefont {Xin}\ \emph {et~al.}(2019)\citenamefont {Xin},
  \citenamefont {Lu}, \citenamefont {Cao}, \citenamefont {Anikeeva},
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  \BibitemOpen
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  \bibnamefont {Zeng}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
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\bibitem [{\citenamefont {Sehayek}\ \emph {et~al.}(2019)\citenamefont
  {Sehayek}, \citenamefont {Golubeva}, \citenamefont {Albergo}, \citenamefont
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  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Dan}\ \bibnamefont
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  {Kulchytskyy}}, \bibinfo {author} {\bibfnamefont {Giacomo}\ \bibnamefont
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  scaling of quantum states: Restricted boltzmann machines},}\ }\href {\doibase
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\bibitem [{\citenamefont {Torlai}\ \emph {et~al.}(2020)\citenamefont {Torlai},
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  \BibitemOpen
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  {Carleo}}, \ and\ \bibinfo {author} {\bibfnamefont {Antonio}\ \bibnamefont
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\bibitem [{\citenamefont {Melkani}\ \emph {et~al.}(2020)\citenamefont
  {Melkani}, \citenamefont {Gneiting},\ and\ \citenamefont
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\bibitem [{\citenamefont {{Ahmed}}\ \emph {et~al.}(2020)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {Tiunov}\ \emph {et~al.}(2020)\citenamefont {Tiunov},
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  \BibitemOpen
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\bibitem [{\citenamefont {{Cha}}\ \emph {et~al.}(2020)\citenamefont {{Cha}},
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  \BibitemOpen
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  [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Neugebauer}\ \emph {et~al.}(2020)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {De~Vlugt}\ \emph {et~al.}(2020)\citenamefont
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  \citenamefont {Roy},\ and\ \citenamefont {Melko}}]{DeVlugt2020}%
  \BibitemOpen
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\bibitem [{\citenamefont {{Smith}}\ \emph {et~al.}(2020)\citenamefont
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  \BibitemOpen
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  [quant-ph]} \BibitemShut {NoStop}%
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  [quant-ph]} \BibitemShut {NoStop}%
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  \BibitemOpen
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\bibitem [{\citenamefont {Ahmed}\ \emph {et~al.}(2020)\citenamefont {Ahmed},
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  \BibitemOpen
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\bibitem [{\citenamefont {Snyder}\ \emph {et~al.}(2012)\citenamefont {Snyder},
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  \BibitemOpen
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  \bibinfo {author} {\bibfnamefont {Kieron}\ \bibnamefont {Burke}},\ }\bibfield
   {title} {\enquote {\bibinfo {title} {Finding density functionals with
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  {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf
  {\bibinfo {volume} {108}},\ \bibinfo {pages} {253002} (\bibinfo {year}
  {2012})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Snyder}\ \emph {et~al.}(2013)\citenamefont {Snyder},
  \citenamefont {Rupp}, \citenamefont {Hansen}, \citenamefont {Blooston},
  \citenamefont {Müller},\ and\ \citenamefont
  {Burke}}]{doi:10.1063/1.4834075}%
  \BibitemOpen
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\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2016)\citenamefont {Li},
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  \BibitemOpen
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  \BibitemOpen
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  \BibitemOpen
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\bibitem [{\citenamefont {Iso}\ \emph {et~al.}(2018)\citenamefont {Iso},
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  {Wang}(2018)}]{PhysRevLett.121.260601}%
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\bibitem [{\citenamefont {Hu}\ \emph {et~al.}(2020)\citenamefont {Hu},
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  {{Kao}}(2020)}]{2020arXiv201005703C}%
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  \BibitemOpen
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  \BibitemOpen
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  {Poulin}(2019)}]{PhysRevLett.122.200501}%
  \BibitemOpen
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  {\doibase 10.1103/PhysRevLett.122.200501} {\bibfield  {journal} {\bibinfo
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  \BibitemOpen
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  \BibitemOpen
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  \BibitemOpen
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  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Xiaotong}\
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\bibitem [{\citenamefont {Davaasuren}\ \emph {et~al.}(2020)\citenamefont
  {Davaasuren}, \citenamefont {Suzuki}, \citenamefont {Fujii},\ and\
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  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Amarsanaa}\
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\bibitem [{\citenamefont {Fitzek}\ \emph {et~al.}(2020)\citenamefont {Fitzek},
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  \BibitemOpen
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\bibitem [{\citenamefont {You}\ \emph {et~al.}(2018)\citenamefont {You},
  \citenamefont {Yang},\ and\ \citenamefont {Qi}}]{PhysRevB.97.045153}%
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  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Yi-Zhuang}\
  \bibnamefont {You}}, \bibinfo {author} {\bibfnamefont {Zhao}\ \bibnamefont
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  (\bibinfo {year} {2018})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Flurin}\ \emph {et~al.}(2020)\citenamefont {Flurin},
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\bibitem [{\citenamefont {{Hashimoto}}\ \emph {et~al.}(2020)\citenamefont
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  {Sutskever}, \citenamefont {Lillicrap}, \citenamefont {Leach}, \citenamefont
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\bibitem [{\citenamefont {Bukov}\ \emph
  {et~al.}(2018{\natexlab{b}})\citenamefont {Bukov}, \citenamefont {Day},
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  \BibitemOpen
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\bibitem [{\citenamefont {Schau{\ss}}\ \emph {et~al.}(2015)\citenamefont
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  {Hild}, \citenamefont {Cheneau}, \citenamefont {Macr{\`\i}}, \citenamefont
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  {title} {\enquote {\bibinfo {title} {Complex density wave orders and quantum
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  \BibitemOpen
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\bibitem [{\citenamefont {White}(1993)}]{PhysRevB.48.10345}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Steven~R.}\
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  {journal} {Phys. Rev. B}\ }\textbf {\bibinfo {volume} {48}},\ \bibinfo
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\bibitem [{\citenamefont {Schollwoeck}(2011)}]{SCHOLLWOCK201196}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Ulrich}\ \bibnamefont
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  }\href {\doibase https://doi.org/10.1016/j.aop.2010.09.012} {\bibfield
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\bibitem [{\citenamefont {{Fishman}}\ \emph {et~al.}(2020)\citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {Ferris}\ and\ \citenamefont
  {Vidal}(2012)}]{PhysRevB.85.165146}%
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\bibitem [{\citenamefont {Basko}\ \emph {et~al.}(2006)\citenamefont {Basko},
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\bibitem [{\citenamefont {Kottmann}\ \emph {et~al.}(2020)\citenamefont
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  \BibitemOpen
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  {\bibfnamefont {Yuan}\ \bibnamefont {Yu}}, \ and\ \bibinfo {author}
  {\bibfnamefont {Xiaoqiang}\ \bibnamefont {Zheng}},\ }\href
  {http://tensorflow.org/} {\enquote {\bibinfo {title} {{TensorFlow}:
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  tensorflow.org}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Eisert}\ \emph {et~al.}(2020)\citenamefont {Eisert},
  \citenamefont {Hangleiter}, \citenamefont {Walk}, \citenamefont {Roth},
  \citenamefont {Markham}, \citenamefont {Parekh}, \citenamefont {Chabaud},\
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  \BibitemOpen
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  {\enquote {\bibinfo {title} {Quantum certification and benchmarking},}\
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\bibitem [{\citenamefont {Knill}\ \emph {et~al.}(2008)\citenamefont {Knill},
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  \citenamefont {Blakestad}, \citenamefont {Jost}, \citenamefont {Langer},
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\bibitem [{\citenamefont {Magesan}\ \emph {et~al.}(2012)\citenamefont
  {Magesan}, \citenamefont {Gambetta},\ and\ \citenamefont
  {Emerson}}]{PhysRevA.85.042311}%
  \BibitemOpen
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\bibitem [{\citenamefont {Harper}\ \emph {et~al.}(2019)\citenamefont {Harper},
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  {Liu}(2011)}]{PhysRevLett.106.230501}%
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\bibitem [{\citenamefont {Aolita}\ \emph {et~al.}(2015)\citenamefont {Aolita},
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  \BibitemOpen
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  {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo
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  \BibitemOpen
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\bibitem [{\citenamefont {\ifmmode \check{R}\else
  \v{R}\fi{}eh\'a\ifmmode~\check{c}\else \v{c}\fi{}ek}\ \emph
  {et~al.}(2001)\citenamefont {\ifmmode \check{R}\else
  \v{R}\fi{}eh\'a\ifmmode~\check{c}\else \v{c}\fi{}ek}, \citenamefont
  {Hradil},\ and\ \citenamefont {Je\ifmmode~\check{z}\else
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  \BibitemOpen
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\bibitem [{\citenamefont {James}\ \emph {et~al.}(2001)\citenamefont {James},
  \citenamefont {Kwiat}, \citenamefont {Munro},\ and\ \citenamefont
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  \BibitemOpen
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\bibitem [{\citenamefont {Je{\v{z}}ek}\ \emph {et~al.}(2003)\citenamefont
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  \BibitemOpen
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  \BibitemOpen
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\bibitem [{\citenamefont {Smolin}\ \emph {et~al.}(2012)\citenamefont {Smolin},
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  {Smith}}]{PhysRevLett.108.070502}%
  \BibitemOpen
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  {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf
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  {2012})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Granade}\ \emph {et~al.}(2017)\citenamefont
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  {Flammia}}]{Granade_2017}%
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  \bibnamefont {Flammia}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
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  10.1088/1367-2630/aa8fe6} {\bibfield  {journal} {\bibinfo  {journal} {New
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\bibitem [{\citenamefont {Nielsen}\ and\ \citenamefont
  {Chuang}(2010)}]{nielsen_chuang_2010}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Michael~A.}\
  \bibnamefont {Nielsen}}\ and\ \bibinfo {author} {\bibfnamefont {Isaac~L.}\
  \bibnamefont {Chuang}},\ }\href {\doibase 10.1017/CBO9780511976667} {\emph
  {\bibinfo {title} {Quantum Computation and Quantum Information: 10th
  Anniversary Edition}}}\ (\bibinfo  {publisher} {Cambridge University Press},\
  \bibinfo {year} {2010})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Häffner}\ \emph {et~al.}(2005)\citenamefont
  {Häffner}, \citenamefont {Hänsel}, \citenamefont {Roos}, \citenamefont
  {Benhelm}, \citenamefont {Chek-al kar}, \citenamefont {Chwalla},
  \citenamefont {Körber}, \citenamefont {Rapol}, \citenamefont {Riebe},
  \citenamefont {Schmidt}, \citenamefont {Becher}, \citenamefont {Gühne},
  \citenamefont {Dür},\ and\ \citenamefont {Blatt}}]{haffner_scalable_2005}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {H.}~\bibnamefont
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  {author} {\bibfnamefont {J.}~\bibnamefont {Benhelm}}, \bibinfo {author}
  {\bibfnamefont {D.}~\bibnamefont {Chek-al kar}}, \bibinfo {author}
  {\bibfnamefont {M.}~\bibnamefont {Chwalla}}, \bibinfo {author} {\bibfnamefont
  {T.}~\bibnamefont {Körber}}, \bibinfo {author} {\bibfnamefont {U.~D.}\
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  {\bibfnamefont {W.}~\bibnamefont {Dür}}, \ and\ \bibinfo {author}
  {\bibfnamefont {R.}~\bibnamefont {Blatt}},\ }\bibfield  {title} {\enquote
  {\bibinfo {title} {Scalable multiparticle entanglement of trapped ions},}\
  }\href {\doibase 10.1038/nature04279} {\bibfield  {journal} {\bibinfo
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  {643--646} (\bibinfo {year} {2005})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gross}\ \emph {et~al.}(2010)\citenamefont {Gross},
  \citenamefont {Liu}, \citenamefont {Flammia}, \citenamefont {Becker},\ and\
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  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {David}\ \bibnamefont
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  \bibinfo {author} {\bibfnamefont {Stephen}\ \bibnamefont {Becker}}, \ and\
  \bibinfo {author} {\bibfnamefont {Jens}\ \bibnamefont {Eisert}},\ }\bibfield
  {title} {\enquote {\bibinfo {title} {Quantum state tomography via compressed
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  {2010})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Flammia}\ \emph {et~al.}(2012)\citenamefont
  {Flammia}, \citenamefont {Gross}, \citenamefont {Liu},\ and\ \citenamefont
  {Eisert}}]{Flammia_2012}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Steven~T}\
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  \bibnamefont {Liu}}, \ and\ \bibinfo {author} {\bibfnamefont {Jens}\
  \bibnamefont {Eisert}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
  {Quantum tomography via compressed sensing: error bounds, sample complexity
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  {\bibfield  {journal} {\bibinfo  {journal} {New Journal of Physics}\ }\textbf
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\bibitem [{\citenamefont {Shabani}\ \emph {et~al.}(2011)\citenamefont
  {Shabani}, \citenamefont {Kosut}, \citenamefont {Mohseni}, \citenamefont
  {Rabitz}, \citenamefont {Broome}, \citenamefont {Almeida}, \citenamefont
  {Fedrizzi},\ and\ \citenamefont {White}}]{PhysRevLett.106.100401}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont
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  \bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Mohseni}}, \bibinfo
  {author} {\bibfnamefont {H.}~\bibnamefont {Rabitz}}, \bibinfo {author}
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  {\bibfnamefont {M.~P.}\ \bibnamefont {Almeida}}, \bibinfo {author}
  {\bibfnamefont {A.}~\bibnamefont {Fedrizzi}}, \ and\ \bibinfo {author}
  {\bibfnamefont {A.~G.}\ \bibnamefont {White}},\ }\bibfield  {title} {\enquote
  {\bibinfo {title} {Efficient measurement of quantum dynamics via compressive
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  {2011})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Riofrío}\ \emph {et~al.}(2017)\citenamefont
  {Riofrío}, \citenamefont {Gross}, \citenamefont {Flammia}, \citenamefont
  {Monz}, \citenamefont {Nigg}, \citenamefont {Blatt},\ and\ \citenamefont
  {Eisert}}]{riofrio_experimental_2017}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.~A.}\ \bibnamefont
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  \bibinfo {author} {\bibfnamefont {S.~T.}\ \bibnamefont {Flammia}}, \bibinfo
  {author} {\bibfnamefont {T.}~\bibnamefont {Monz}}, \bibinfo {author}
  {\bibfnamefont {D.}~\bibnamefont {Nigg}}, \bibinfo {author} {\bibfnamefont
  {R.}~\bibnamefont {Blatt}}, \ and\ \bibinfo {author} {\bibfnamefont
  {J.}~\bibnamefont {Eisert}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
  {Experimental quantum compressed sensing for a seven-qubit system},}\ }\href
  {\doibase 10.1038/ncomms15305} {\bibfield  {journal} {\bibinfo  {journal}
  {Nature Communications}\ }\textbf {\bibinfo {volume} {8}},\ \bibinfo {pages}
  {15305} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {T\'oth}\ \emph {et~al.}(2010)\citenamefont {T\'oth},
  \citenamefont {Wieczorek}, \citenamefont {Gross}, \citenamefont {Krischek},
  \citenamefont {Schwemmer},\ and\ \citenamefont
  {Weinfurter}}]{PhysRevLett.105.250403}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont
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  {\bibfnamefont {C.}~\bibnamefont {Schwemmer}}, \ and\ \bibinfo {author}
  {\bibfnamefont {H.}~\bibnamefont {Weinfurter}},\ }\bibfield  {title}
  {\enquote {\bibinfo {title} {Permutationally invariant quantum tomography},}\
  }\href {\doibase 10.1103/PhysRevLett.105.250403} {\bibfield  {journal}
  {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {105}},\
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\bibitem [{\citenamefont {Moroder}\ \emph {et~al.}(2012)\citenamefont
  {Moroder}, \citenamefont {Hyllus}, \citenamefont {T{\'{o}}th}, \citenamefont
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  {Gühne},\ and\ \citenamefont {Weinfurter}}]{Moroder_2012}%
  \BibitemOpen
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  {Gaile}}, \bibinfo {author} {\bibfnamefont {Otfried}\ \bibnamefont {Gühne}},
  \ and\ \bibinfo {author} {\bibfnamefont {Harald}\ \bibnamefont
  {Weinfurter}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
  {Permutationally invariant state reconstruction},}\ }\href {\doibase
  10.1088/1367-2630/14/10/105001} {\bibfield  {journal} {\bibinfo  {journal}
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\bibitem [{\citenamefont {Cramer}\ \emph {et~al.}(2009)\citenamefont {Cramer},
  \citenamefont {Plenio}, \citenamefont {Flammia}, \citenamefont {Somma},
  \citenamefont {Gross}, \citenamefont {Bartlett}, \citenamefont
  {Landon-Cardinal}, \citenamefont {Poulin},\ and\ \citenamefont
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  \BibitemOpen
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  {O}~\bibnamefont {Landon-Cardinal}}, \bibinfo {author} {\bibfnamefont
  {D}~\bibnamefont {Poulin}}, \ and\ \bibinfo {author} {\bibfnamefont
  {YK}~\bibnamefont {Liu}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
  {Efficient quantum state tomography.}}\ }\href
  {http://www.nature.com/articles/ncomms1147} {\bibfield  {journal} {\bibinfo
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  \bibinfo {pages} {149} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Baumgratz}\ \emph {et~al.}(2013)\citenamefont
  {Baumgratz}, \citenamefont {Gross}, \citenamefont {Cramer},\ and\
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  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {T.}~\bibnamefont
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  {\enquote {\bibinfo {title} {Scalable reconstruction of density matrices},}\
  }\href {\doibase 10.1103/PhysRevLett.111.020401} {\bibfield  {journal}
  {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {111}},\
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\bibitem [{\citenamefont {Lanyon}\ \emph {et~al.}(2017)\citenamefont {Lanyon},
  \citenamefont {Maier}, \citenamefont {Holz{\"{a}}pfel}, \citenamefont
  {Baumgratz}, \citenamefont {Hempel}, \citenamefont {Jurcevic}, \citenamefont
  {Dhand}, \citenamefont {Buyskikh}, \citenamefont {Daley}, \citenamefont
  {Cramer}, \citenamefont {Plenio}, \citenamefont {Blatt},\ and\ \citenamefont
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  \BibitemOpen
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  {\bibfnamefont {P.}~\bibnamefont {Jurcevic}}, \bibinfo {author}
  {\bibfnamefont {I.}~\bibnamefont {Dhand}}, \bibinfo {author} {\bibfnamefont
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  \bibinfo {author} {\bibfnamefont {R.}~\bibnamefont {Blatt}}, \ and\ \bibinfo
  {author} {\bibfnamefont {C.~F.}\ \bibnamefont {Roos}},\ }\bibfield  {title}
  {\enquote {\bibinfo {title} {{Efficient tomography of a quantum many-body
  system}},}\ }\href {\doibase 10.1038/nphys4244} {\bibfield  {journal}
  {\bibinfo  {journal} {Nature Physics}\ }\textbf {\bibinfo {volume} {13}},\
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\bibitem [{\citenamefont {Wang}\ \emph {et~al.}(2020)\citenamefont {Wang},
  \citenamefont {Han}, \citenamefont {Wang}, \citenamefont {Li}, \citenamefont
  {Mu}, \citenamefont {Fan},\ and\ \citenamefont {Wang}}]{LeiWang2020}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Jun}\ \bibnamefont
  {Wang}}, \bibinfo {author} {\bibfnamefont {Zhao-Yu}\ \bibnamefont {Han}},
  \bibinfo {author} {\bibfnamefont {Song-Bo}\ \bibnamefont {Wang}}, \bibinfo
  {author} {\bibfnamefont {Zeyang}\ \bibnamefont {Li}}, \bibinfo {author}
  {\bibfnamefont {Liang-Zhu}\ \bibnamefont {Mu}}, \bibinfo {author}
  {\bibfnamefont {Heng}\ \bibnamefont {Fan}}, \ and\ \bibinfo {author}
  {\bibfnamefont {Lei}\ \bibnamefont {Wang}},\ }\bibfield  {title} {\enquote
  {\bibinfo {title} {Scalable quantum tomography with fidelity estimation},}\
  }\href {\doibase 10.1103/PhysRevA.101.032321} {\bibfield  {journal} {\bibinfo
   {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {101}},\ \bibinfo
  {pages} {032321} (\bibinfo {year} {2020})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Ackley}\ \emph {et~al.}(1985)\citenamefont {Ackley},
  \citenamefont {Hinton},\ and\ \citenamefont {Sejnowski}}]{Ackley85}%
  \BibitemOpen
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  \bibnamefont {Ackley}}, \bibinfo {author} {\bibfnamefont {Geoffrey~E.}\
  \bibnamefont {Hinton}}, \ and\ \bibinfo {author} {\bibfnamefont
  {Terrence~J.}\ \bibnamefont {Sejnowski}},\ }\bibfield  {title} {\enquote
  {\bibinfo {title} {A learning algorithm for boltzmann machines},}\ }\href
  {\doibase https://doi.org/10.1016/S0364-0213(85)80012-4} {\bibfield
  {journal} {\bibinfo  {journal} {Cognitive Science}\ }\textbf {\bibinfo
  {volume} {9}},\ \bibinfo {pages} {147 -- 169} (\bibinfo {year}
  {1985})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Smolensky}(1986)}]{Smolensky1986}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont
  {Smolensky}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Parallel
  distributed processing: Explorations in the microstructure of cognition, vol.
  1},}\ }in\ \href {http://dl.acm.org/citation.cfm?id=104279.104290} {\emph
  {\bibinfo {booktitle} {Parallel Distributed Processing}}},\ \bibinfo {editor}
  {edited by\ \bibinfo {editor} {\bibfnamefont {David~E.}\ \bibnamefont
  {Rumelhart}}, \bibinfo {editor} {\bibfnamefont {James~L.}\ \bibnamefont
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  \bibnamefont {PDP Research~Group}}}\ (\bibinfo  {publisher} {MIT Press},\
  \bibinfo {address} {Cambridge, MA, USA},\ \bibinfo {year} {1986})\ Chap.\
  \bibinfo {chapter} {Information Processing in Dynamical Systems: Foundations
  of Harmony Theory}, pp.\ \bibinfo {pages} {194--281}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Little}(1974)}]{Little74}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.A.}\ \bibnamefont
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  https://doi.org/10.1016/0025-5564(74)90031-5} {\bibfield  {journal} {\bibinfo
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\bibitem [{\citenamefont {Little}\ and\ \citenamefont {Shaw}(1978)}]{Little78}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.A.}\ \bibnamefont
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\bibitem [{\citenamefont {Hopfield}(1982)}]{Hopfield82}%
  \BibitemOpen
  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {J~J}\ \bibnamefont
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  }\textbf {\bibinfo {volume} {79}},\ \bibinfo {pages} {2554--2558} (\bibinfo
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\bibitem [{\citenamefont {Le~Roux}\ and\ \citenamefont
  {Bengio}(2008)}]{LeRoux2008}%
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\bibitem [{\citenamefont {Kullback}\ and\ \citenamefont
  {Leibler}(1951)}]{Kullback:1951aa}%
  \BibitemOpen
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  {1951})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {{Bravyi}}\ \emph {et~al.}(2006)\citenamefont
  {{Bravyi}}, \citenamefont {{DiVincenzo}}, \citenamefont {{Oliveira}},\ and\
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  \BibitemOpen
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  {{Oliveira}}}, \ and\ \bibinfo {author} {\bibfnamefont {Barbara~M.}\
  \bibnamefont {{Terhal}}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
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  {\bibfield  {journal} {\bibinfo  {journal} {arXiv e-prints}\ ,\ \bibinfo
  {eid} {quant-ph/0606140}} (\bibinfo {year} {2006})},\ \Eprint
  {http://arxiv.org/abs/quant-ph/0606140} {arXiv:quant-ph/0606140 [quant-ph]}
  \BibitemShut {NoStop}%
\bibitem [{\citenamefont {{Carleo}}\ \emph {et~al.}(2019)\citenamefont
  {{Carleo}}, \citenamefont {{Choo}}, \citenamefont {{Hofmann}}, \citenamefont
  {{Smith}}, \citenamefont {{Westerhout}}, \citenamefont {{Alet}},
  \citenamefont {{Davis}}, \citenamefont {{Efthymiou}}, \citenamefont
  {{Glasser}}, \citenamefont {{Lin}}, \citenamefont {{Mauri}}, \citenamefont
  {{Mazzola}}, \citenamefont {{Mendl}}, \citenamefont {{van Nieuwenburg}},
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  {{Torlai}},\ and\ \citenamefont {{Wietek}}}]{netket}%
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  \bibinfo {author} {\bibfnamefont {Ossian}\ \bibnamefont {{O'Reilly}}},
  \bibinfo {author} {\bibfnamefont {Hugo}\ \bibnamefont {{Th{\'e}veniaut}}},
  \bibinfo {author} {\bibfnamefont {Giacomo}\ \bibnamefont {{Torlai}}}, \ and\
  \bibinfo {author} {\bibfnamefont {Alexander}\ \bibnamefont {{Wietek}}},\
  }\bibfield  {title} {\enquote {\bibinfo {title} {{NetKet: A Machine Learning
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\bibitem [{\citenamefont {Kandala}\ \emph {et~al.}(2017)\citenamefont
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  {Gambetta}}]{kandala_hardware-efficient_2017}%
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  \bibfield  {author} {\bibinfo {author} {\bibfnamefont {Abhinav}\ \bibnamefont
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  {Temme}}, \bibinfo {author} {\bibfnamefont {Maika}\ \bibnamefont {Takita}},
  \bibinfo {author} {\bibfnamefont {Markus}\ \bibnamefont {Brink}}, \bibinfo
  {author} {\bibfnamefont {Jerry~M.}\ \bibnamefont {Chow}}, \ and\ \bibinfo
  {author} {\bibfnamefont {Jay~M.}\ \bibnamefont {Gambetta}},\ }\bibfield
  {title} {\enquote {\bibinfo {title} {Hardware-efficient variational quantum
  eigensolver for small molecules and quantum magnets},}\ }\href {\doibase
  10.1038/nature23879} {\bibfield  {journal} {\bibinfo  {journal} {Nature}\
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  \citenamefont {van Merri{\"e}nboer}, \citenamefont {Gulcehre}, \citenamefont
  {Bahdanau}, \citenamefont {Bougares}, \citenamefont {Schwenk},\ and\
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  \bibnamefont {Gulcehre}}, \bibinfo {author} {\bibfnamefont {Dzmitry}\
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  \bibnamefont {Bougares}}, \bibinfo {author} {\bibfnamefont {Holger}\
  \bibnamefont {Schwenk}}, \ and\ \bibinfo {author} {\bibfnamefont {Yoshua}\
  \bibnamefont {Bengio}},\ }\bibfield  {title} {\enquote {\bibinfo {title}
  {Learning phrase representations using {RNN} encoder{--}decoder for
  statistical machine translation},}\ }in\ \href {\doibase 10.3115/v1/D14-1179}
  {\emph {\bibinfo {booktitle} {Proceedings of the 2014 Conference on Empirical
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