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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {P.W.}\ \bibnamefont {Shor}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Algorithms for quantum computation: discrete logarithms and factoring},}\ }in\ \href {\doibase 10.1109/SFCS.1994.365700} {\emph {\bibinfo {booktitle} {Proceedings 35th Annual Symposium on Foundations of Computer Science}}}\ (\bibinfo {year} {1994})\ pp.\ \bibinfo {pages} {124--134}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Jiang}\ \emph {et~al.}(2018)\citenamefont {Jiang}, \citenamefont {Britt}, \citenamefont {McCaskey}, \citenamefont {Humble},\ and\ \citenamefont {Kais}}]{Jiang2018}%
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\bibitem [{\citenamefont {Pirnay}\ \emph {et~al.}(2023)\citenamefont {Pirnay}, \citenamefont {Ulitzsch}, \citenamefont {Wilde}, \citenamefont {Eisert},\ and\ \citenamefont {Seifert}}]{pirnay2023inprinciple}%
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\bibitem [{\citenamefont {Kirby}\ \emph {et~al.}(2023)\citenamefont {Kirby}, \citenamefont {Motta},\ and\ \citenamefont {Mezzacapo}}]{Kirby_2023}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {William}\ \bibnamefont {Kirby}}, \bibinfo {author} {\bibfnamefont {Mario}\ \bibnamefont {Motta}}, \ and\ \bibinfo {author} {\bibfnamefont {Antonio}\ \bibnamefont {Mezzacapo}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Exact and efficient lanczos method on a quantum computer},}\ }\href {\doibase 10.22331/q-2023-05-23-1018} {\bibfield  {journal} {\bibinfo  {journal} {Quantum}\ }\textbf {\bibinfo {volume} {7}},\ \bibinfo {pages} {1018} (\bibinfo {year} {2023})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lloyd}(1996)}]{Lloyd1996universal}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Seth}\ \bibnamefont {Lloyd}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Universal quantum simulators},}\ }\href {\doibase 10.1126/science.273.5278.1073} {\bibfield  {journal} {\bibinfo  {journal} {Science}\ }\textbf {\bibinfo {volume} {273}},\ \bibinfo {pages} {1073--1078} (\bibinfo {year} {1996})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Childs}\ \emph {et~al.}(2003)\citenamefont {Childs}, \citenamefont {Cleve}, \citenamefont {Deotto}, \citenamefont {Farhi}, \citenamefont {Gutmann},\ and\ \citenamefont {Spielman}}]{Childs2002qw}%
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\bibitem [{\citenamefont {Berry}\ \emph {et~al.}(2007)\citenamefont {Berry}, \citenamefont {Ahokas}, \citenamefont {Cleve},\ and\ \citenamefont {Sanders}}]{Berry2007sparse}%
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\bibitem [{\citenamefont {Harrow}\ \emph {et~al.}(2009)\citenamefont {Harrow}, \citenamefont {Hassidim},\ and\ \citenamefont {Lloyd}}]{Harrow2009linear}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Aram~W.}\ \bibnamefont {Harrow}}, \bibinfo {author} {\bibfnamefont {Avinatan}\ \bibnamefont {Hassidim}}, \ and\ \bibinfo {author} {\bibfnamefont {Seth}\ \bibnamefont {Lloyd}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum algorithm for linear systems of equations},}\ }\href {\doibase 10.1103/PhysRevLett.103.150502} {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {103}},\ \bibinfo {pages} {150502} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Childs}\ \emph {et~al.}(2017)\citenamefont {Childs}, \citenamefont {Kothari},\ and\ \citenamefont {Somma}}]{childs2017quantum}%
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\bibitem [{\citenamefont {Lawson}\ \emph {et~al.}(1979)\citenamefont {Lawson}, \citenamefont {Hanson}, \citenamefont {Kincaid},\ and\ \citenamefont {Krogh}}]{Lawson1979BLAS}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {C.~L.}\ \bibnamefont {Lawson}}, \bibinfo {author} {\bibfnamefont {R.~J.}\ \bibnamefont {Hanson}}, \bibinfo {author} {\bibfnamefont {D.~R.}\ \bibnamefont {Kincaid}}, \ and\ \bibinfo {author} {\bibfnamefont {F.~T.}\ \bibnamefont {Krogh}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Basic linear algebra subprograms for fortran usage},}\ }\href {\doibase 10.1145/355841.355847} {\bibfield  {journal} {\bibinfo  {journal} {ACM Trans. Math. Softw.}\ }\textbf {\bibinfo {volume} {5}},\ \bibinfo {pages} {308–323} (\bibinfo {year} {1979})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Low}\ and\ \citenamefont {Chuang}(2017)}]{Low2017Optimal}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Guang~Hao}\ \bibnamefont {Low}}\ and\ \bibinfo {author} {\bibfnamefont {Isaac~L.}\ \bibnamefont {Chuang}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Optimal hamiltonian simulation by quantum signal processing},}\ }\href {\doibase 10.1103/PhysRevLett.118.010501} {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {118}},\ \bibinfo {pages} {010501} (\bibinfo {year} {2017})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gily{\'e}n}\ \emph {et~al.}(2019)\citenamefont {Gily{\'e}n}, \citenamefont {Su}, \citenamefont {Low},\ and\ \citenamefont {Wiebe}}]{gilyen2019quantum}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Andr{\'a}s}\ \bibnamefont {Gily{\'e}n}}, \bibinfo {author} {\bibfnamefont {Yuan}\ \bibnamefont {Su}}, \bibinfo {author} {\bibfnamefont {Guang~Hao}\ \bibnamefont {Low}}, \ and\ \bibinfo {author} {\bibfnamefont {Nathan}\ \bibnamefont {Wiebe}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics},}\ }in\ \href@noop {} {\emph {\bibinfo {booktitle} {Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing}}}\ (\bibinfo {year} {2019})\ pp.\ \bibinfo {pages} {193--204}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Geman}\ and\ \citenamefont {Geman}(1984)}]{Geman1984-yy}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Stuart}\ \bibnamefont {Geman}}\ and\ \bibinfo {author} {\bibfnamefont {Donald}\ \bibnamefont {Geman}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Stochastic relaxation, gibbs distributions, and the bayesian restoration of images},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {IEEE Trans. Pattern Anal. Mach. Intell.}\ }\textbf {\bibinfo {volume} {PAMI-6}},\ \bibinfo {pages} {721--741} (\bibinfo {year} {1984})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Krzaka{\l}a}\ \emph {et~al.}(2007)\citenamefont {Krzaka{\l}a}, \citenamefont {Montanari}, \citenamefont {Ricci-Tersenghi}, \citenamefont {Semerjian},\ and\ \citenamefont {Zdeborov{\'a}}}]{krzakala2007gibbs}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Florent}\ \bibnamefont {Krzaka{\l}a}}, \bibinfo {author} {\bibfnamefont {Andrea}\ \bibnamefont {Montanari}}, \bibinfo {author} {\bibfnamefont {Federico}\ \bibnamefont {Ricci-Tersenghi}}, \bibinfo {author} {\bibfnamefont {Guilhem}\ \bibnamefont {Semerjian}}, \ and\ \bibinfo {author} {\bibfnamefont {Lenka}\ \bibnamefont {Zdeborov{\'a}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Gibbs states and the set of solutions of random constraint satisfaction problems},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Proceedings of the National Academy of Sciences}\ }\textbf {\bibinfo {volume} {104}},\ \bibinfo {pages} {10318--10323} (\bibinfo {year} {2007})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Stockmeyer}(1983)}]{Stockmeyer1983}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Larry}\ \bibnamefont {Stockmeyer}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The complexity of approximate counting},}\ }in\ \href {\doibase 10.1145/800061.808740} {\emph {\bibinfo {booktitle} {Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC ’83}}},\ \bibinfo {series and number} {STOC ’83}\ (\bibinfo  {publisher} {ACM Press},\ \bibinfo {year} {1983})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Zhang}\ \emph {et~al.}(2023)\citenamefont {Zhang}, \citenamefont {Bosse},\ and\ \citenamefont {Cubitt}}]{zhang2023dissipative}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Daniel}\ \bibnamefont {Zhang}}, \bibinfo {author} {\bibfnamefont {Jan~Lukas}\ \bibnamefont {Bosse}}, \ and\ \bibinfo {author} {\bibfnamefont {Toby}\ \bibnamefont {Cubitt}},\ }\href@noop {} {\enquote {\bibinfo {title} {Dissipative quantum gibbs sampling},}\ } (\bibinfo {year} {2023}),\ \Eprint {http://arxiv.org/abs/2304.04526} {arXiv:2304.04526 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Metropolis}\ \emph {et~al.}(1953)\citenamefont {Metropolis}, \citenamefont {Rosenbluth}, \citenamefont {Rosenbluth}, \citenamefont {Teller},\ and\ \citenamefont {Teller}}]{Metropolis1953}%
\BibitemOpen
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\bibitem [{\citenamefont {Hastings}(1970)}]{Hastings1970}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {W.~K.}\ \bibnamefont {Hastings}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {{Monte Carlo sampling methods using Markov chains and their applications}},}\ }\href {\doibase 10.1093/biomet/57.1.97} {\bibfield  {journal} {\bibinfo  {journal} {Biometrika}\ }\textbf {\bibinfo {volume} {57}},\ \bibinfo {pages} {97–109} (\bibinfo {year} {1970})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Poulin}\ and\ \citenamefont {Wocjan}(2009)}]{poulin2009sampling}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {David}\ \bibnamefont {Poulin}}\ and\ \bibinfo {author} {\bibfnamefont {Pawel}\ \bibnamefont {Wocjan}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Sampling from the thermal quantum gibbs state and evaluating partition functions with a quantum computer},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Physical review letters}\ }\textbf {\bibinfo {volume} {103}},\ \bibinfo {pages} {220502} (\bibinfo {year} {2009})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Aharonov}\ \emph {et~al.}(2013{\natexlab{b}})\citenamefont {Aharonov}, \citenamefont {Arad},\ and\ \citenamefont {Vidick}}]{aharonov2013quantum}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Dorit}\ \bibnamefont {Aharonov}}, \bibinfo {author} {\bibfnamefont {Itai}\ \bibnamefont {Arad}}, \ and\ \bibinfo {author} {\bibfnamefont {Thomas}\ \bibnamefont {Vidick}},\ }\href@noop {} {\enquote {\bibinfo {title} {The quantum pcp conjecture},}\ } (\bibinfo {year} {2013}{\natexlab{b}}),\ \Eprint {http://arxiv.org/abs/1309.7495} {arXiv:1309.7495 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Bravyi}\ \emph {et~al.}(2022{\natexlab{a}})\citenamefont {Bravyi}, \citenamefont {Chowdhury}, \citenamefont {Gosset},\ and\ \citenamefont {Wocjan}}]{bravyi2021complexity}%
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\bibitem [{\citenamefont {Terhal}\ and\ \citenamefont {DiVincenzo}(2000)}]{terhal2000problem}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {F.~G. S.~L.}\ \bibnamefont {{Brandao}}}\ and\ \bibinfo {author} {\bibfnamefont {K.~M.}\ \bibnamefont {{Svore}}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum speed-ups for solving semidefinite programs},}\ }in\ \href {\doibase 10.1109/FOCS.2017.45} {\emph {\bibinfo {booktitle} {2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)}}}\ (\bibinfo {year} {2017})\ pp.\ \bibinfo {pages} {415--426}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {van Apeldoorn}\ \emph {et~al.}(2020{\natexlab{a}})\citenamefont {van Apeldoorn}, \citenamefont {Gilyén}, \citenamefont {Gribling},\ and\ \citenamefont {de~Wolf}}]{vanApeldoorn2020}%
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\bibitem [{\citenamefont {{Brandao}}\ \emph {et~al.}(2019)\citenamefont {{Brandao}}, \citenamefont {Kalev}, \citenamefont {Li}, \citenamefont {Lin}, \citenamefont {{Svore}},\ and\ \citenamefont {Wu}}]{brandao2019quantum}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Ashley}\ \bibnamefont {Montanaro}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum speedup of monte carlo methods},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}\ }\textbf {\bibinfo {volume} {471}},\ \bibinfo {pages} {20150301} (\bibinfo {year} {2015}{\natexlab{a}})}\BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Arunachalam}\ \emph {et~al.}(2022)\citenamefont {Arunachalam}, \citenamefont {Havlicek}, \citenamefont {Nannicini}, \citenamefont {Temme},\ and\ \citenamefont {Wocjan}}]{arunachalam2022simpler}%
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\bibitem [{\citenamefont {Bouland}\ \emph {et~al.}(2023)\citenamefont {Bouland}, \citenamefont {Getachew}, \citenamefont {Jin}, \citenamefont {Sidford},\ and\ \citenamefont {Tian}}]{bouland2023quantum}%
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\bibitem [{\citenamefont {Gao}\ \emph {et~al.}(2023)\citenamefont {Gao}, \citenamefont {Ji}, \citenamefont {Li},\ and\ \citenamefont {Wang}}]{gao2023logarithmicregret}%
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\bibitem [{\citenamefont {Li}\ \emph {et~al.}(2020{\natexlab{a}})\citenamefont {Li}, \citenamefont {Fan}, \citenamefont {Coram}, \citenamefont {Riley},\ and\ \citenamefont {Leichenauer}}]{Li_2020_Gibbs_objective}%
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\bibitem [{\citenamefont {Patti}\ \emph {et~al.}(2023)\citenamefont {Patti}, \citenamefont {Kossaifi}, \citenamefont {Anandkumar},\ and\ \citenamefont {Yelin}}]{Patti_2023}%
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\bibitem [{\citenamefont {Brand{\~{a} }o}\ \emph {et~al.}(2022)\citenamefont {Brand{\~{a} }o}, \citenamefont {Kueng},\ and\ \citenamefont {Fran{\c{c}}a}}]{Brandao_2022}%
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\bibitem [{\citenamefont {Tang}(2019)}]{Tang_2019_recommendation}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Ewin}\ \bibnamefont {Tang}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {A quantum-inspired classical algorithm for recommendation systems},}\ }in\ \href {\doibase 10.1145/3313276.3316310} {\emph {\bibinfo {booktitle} {Proceedings of the 51st Annual {ACM} {SIGACT} Symposium on Theory of Computing}}}\ (\bibinfo  {publisher} {{ACM}},\ \bibinfo {year} {2019})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Chia}\ \emph {et~al.}(2020)\citenamefont {Chia}, \citenamefont {Gily{\'e}n}, \citenamefont {Lin}, \citenamefont {Lloyd}, \citenamefont {Tang},\ and\ \citenamefont {Wang}}]{chia_2020_low_rank_linear}%
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\bibitem [{\citenamefont {Crama}\ \emph {et~al.}(2022)\citenamefont {Crama}, \citenamefont {Elloumi}, \citenamefont {Lambert},\ and\ \citenamefont {Rodriguez-Heck}}]{crama:hal-03795395}%
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\bibitem [{\citenamefont {Karimi}\ and\ \citenamefont {Ronagh}(2019)}]{Karimi_2019_int2bin}%
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\bibitem [{\citenamefont {Biamonte}(2008)}]{biamonte2008nonperturbative}%
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\bibitem [{\citenamefont {Babbush}\ \emph {et~al.}(2013)\citenamefont {Babbush}, \citenamefont {O'Gorman},\ and\ \citenamefont {Aspuru-Guzik}}]{babbush2013resource}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Ryan}\ \bibnamefont {Babbush}}, \bibinfo {author} {\bibfnamefont {Bryan}\ \bibnamefont {O'Gorman}}, \ and\ \bibinfo {author} {\bibfnamefont {Al{\'a}n}\ \bibnamefont {Aspuru-Guzik}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Resource efficient gadgets for compiling adiabatic quantum optimization problems},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Annalen der Physik}\ }\textbf {\bibinfo {volume} {525}},\ \bibinfo {pages} {877--888} (\bibinfo {year} {2013})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Lucas}(2014)}]{Lucas2014}%
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\bibitem [{\citenamefont {Glover}\ \emph {et~al.}(2022{\natexlab{a}})\citenamefont {Glover}, \citenamefont {Kochenberger}, \citenamefont {Hennig},\ and\ \citenamefont {Du}}]{glover2022}%
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\bibitem [{\citenamefont {Peruzzo}\ \emph {et~al.}(2014)\citenamefont {Peruzzo}, \citenamefont {McClean}, \citenamefont {Shadbolt}, \citenamefont {Yung}, \citenamefont {Zhou}, \citenamefont {Love}, \citenamefont {Aspuru-Guzik},\ and\ \citenamefont {O'Brien}}]{Peruzzo2014}%
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\bibitem [{\citenamefont {Barahona}(1982)}]{barahona1982computational}%
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\bibitem [{\citenamefont {Arora}(1998{\natexlab{b}})}]{Arora1998ETSP}%
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\bibitem [{\citenamefont {Farhi}\ \emph {et~al.}(2014)\citenamefont {Farhi}, \citenamefont {Goldstone},\ and\ \citenamefont {Gutmann}}]{Farhi2014}%
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\bibitem [{\citenamefont {Lloyd}(2018)}]{lloyd2018quantum}%
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\bibitem [{\citenamefont {Wurtz}\ and\ \citenamefont {Love}(2021)}]{PhysRevA.103.042612}%
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\bibitem [{\citenamefont {Basso}\ \emph {et~al.}(2022)\citenamefont {Basso}, \citenamefont {Farhi}, \citenamefont {Marwaha}, \citenamefont {Villalonga},\ and\ \citenamefont {Zhou}}]{basso2021quantum}%
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\bibitem [{\citenamefont {Zhou}\ \emph {et~al.}(2020)\citenamefont {Zhou}, \citenamefont {Wang}, \citenamefont {Choi}, \citenamefont {Pichler},\ and\ \citenamefont {Lukin}}]{Zhou2020}%
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\bibitem [{\citenamefont {Sack}\ and\ \citenamefont {Serbyn}(2021)}]{sack2021quantum}%
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\bibitem [{\citenamefont {Scriva}\ \emph {et~al.}(2023)\citenamefont {Scriva}, \citenamefont {Astrakhantsev}, \citenamefont {Pilati},\ and\ \citenamefont {Mazzola}}]{scriva2023challenges}%
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\bibitem [{\citenamefont {Alam}\ \emph {et~al.}(2020{\natexlab{a}})\citenamefont {Alam}, \citenamefont {Ash-Saki},\ and\ \citenamefont {Ghosh}}]{alam2020accelerating}%
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{\bibfnamefont {A.~M.}\ \bibnamefont {Zolot}}, \ and\ \bibinfo {author} {\bibfnamefont {J.~M.}\ \bibnamefont {Pino}},\ }\href {https://arxiv.org/abs/2305.03828} {\enquote {\bibinfo {title} {A race track trapped-ion quantum processor},}\ } (\bibinfo {year} {2023}),\ \Eprint {http://arxiv.org/abs/2305.03828} {arXiv:2305.03828 [quant-ph]} \BibitemShut {NoStop}%
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\bibitem [{\citenamefont {Bravyi}\ \emph {et~al.}(2022{\natexlab{b}})\citenamefont {Bravyi}, \citenamefont {Kliesch}, \citenamefont {Koenig},\ and\ \citenamefont {Tang}}]{Bravyi2020b}%
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\bibitem [{\citenamefont {Dupont}\ \emph {et~al.}(2023)\citenamefont {Dupont}, \citenamefont {Evert}, \citenamefont {Hodson}, \citenamefont {Sundar}, \citenamefont {Jeffrey}, \citenamefont {Yamaguchi}, \citenamefont {Feng}, \citenamefont {Maciejewski}, \citenamefont {Hadfield}, \citenamefont {Alam}, \citenamefont {Wang}, \citenamefont {Grabbe}, \citenamefont {Lott}, \citenamefont {Rieffel}, \citenamefont {Venturelli},\ and\ \citenamefont {Reagor}}]{Dupont_2023QuantumCombOpt}%
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\bibitem [{\citenamefont {Finžgar}\ \emph {et~al.}(2023)\citenamefont {Finžgar}, \citenamefont {Kerschbaumer}, \citenamefont {Schuetz}, \citenamefont {Mendl},\ and\ \citenamefont {Katzgraber}}]{finvzgar2023quantum}%
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\bibitem [{\citenamefont {Farhi}\ \emph {et~al.}(2020)\citenamefont {Farhi}, \citenamefont {Gamarnik},\ and\ \citenamefont {Gutmann}}]{farhi2020quantum}%
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\bibitem [{\citenamefont {Misra-Spieldenner}\ \emph {et~al.}(2023)\citenamefont {Misra-Spieldenner}, \citenamefont {Bode}, \citenamefont {Schuhmacher}, \citenamefont {Stollenwerk}, \citenamefont {Bagrets},\ and\ \citenamefont {Wilhelm}}]{Misra_Spieldenner_2023}%
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\bibitem [{\citenamefont {Blekos}\ \emph {et~al.}(2023)\citenamefont {Blekos}, \citenamefont {Brand}, \citenamefont {Ceschini}, \citenamefont {Chou}, \citenamefont {Li}, \citenamefont {Pandya},\ and\ \citenamefont {Summer}}]{blekos2023review}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Ankit}\ \bibnamefont {Garg}}, \bibinfo {author} {\bibfnamefont {Robin}\ \bibnamefont {Kothari}}, \bibinfo {author} {\bibfnamefont {Praneeth}\ \bibnamefont {Netrapalli}}, \ and\ \bibinfo {author} {\bibfnamefont {Suhail}\ \bibnamefont {Sherif}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Near-optimal lower bounds for convex optimization for all orders of smoothness},}\ }in\ \href {https://proceedings.neurips.cc/paper_files/paper/2021/file/fa6c94460e902005a0b660266190c8ba-Paper.pdf} {\emph {\bibinfo {booktitle} {Advances in Neural Information Processing Systems}}},\ Vol.~\bibinfo {volume} {34},\ \bibinfo {editor} {edited by\ \bibinfo {editor} {\bibfnamefont {M.}~\bibnamefont {Ranzato}}, \bibinfo {editor} {\bibfnamefont {A.}~\bibnamefont {Beygelzimer}}, \bibinfo {editor} {\bibfnamefont {Y.}~\bibnamefont {Dauphin}}, \bibinfo {editor} {\bibfnamefont {P.S.}\ \bibnamefont {Liang}}, \ and\ \bibinfo {editor} {\bibfnamefont {J.~Wortman}\ \bibnamefont {Vaughan}}}\ (\bibinfo  {publisher} {Curran Associates, Inc.},\ \bibinfo {year} {2021})\ pp.\ \bibinfo {pages} {29874--29884}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Gr{\"o}tschel}\ \emph {et~al.}(2012)\citenamefont {Gr{\"o}tschel}, \citenamefont {Lov{\'a}sz},\ and\ \citenamefont {Schrijver}}]{grotschel2012geometric}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Martin}\ \bibnamefont {Gr{\"o}tschel}}, \bibinfo {author} {\bibfnamefont {L{\'a}szl{\'o}}\ \bibnamefont {Lov{\'a}sz}}, \ and\ \bibinfo {author} {\bibfnamefont {Alexander}\ \bibnamefont {Schrijver}},\ }\href@noop {} {\emph {\bibinfo {title} {Geometric algorithms and combinatorial optimization}}},\ Vol.~\bibinfo {volume} {2}\ (\bibinfo  {publisher} {Springer Science \& Business Media},\ \bibinfo {year} {2012})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {van Apeldoorn}\ \emph {et~al.}(2020{\natexlab{b}})\citenamefont {van Apeldoorn}, \citenamefont {Gilyén}, \citenamefont {Gribling},\ and\ \citenamefont {de~Wolf}}]{van2020oracles}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Joran}\ \bibnamefont {van Apeldoorn}}, \bibinfo {author} {\bibfnamefont {András}\ \bibnamefont {Gilyén}}, \bibinfo {author} {\bibfnamefont {Sander}\ \bibnamefont {Gribling}}, \ and\ \bibinfo {author} {\bibfnamefont {Ronald}\ \bibnamefont {de~Wolf}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Convex optimization using quantum oracles},}\ }\href {\doibase 10.22331/q-2020-01-13-220} {\bibfield  {journal} {\bibinfo  {journal} {Quantum}\ }\textbf {\bibinfo {volume} {4}} (\bibinfo {year} {2020}{\natexlab{b}}),\ 10.22331/q-2020-01-13-220}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Chakrabarti}\ \emph {et~al.}(2020)\citenamefont {Chakrabarti}, \citenamefont {Childs}, \citenamefont {Li},\ and\ \citenamefont {Wu}}]{chakrabarti2020quantum}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Shouvanik}\ \bibnamefont {Chakrabarti}}, \bibinfo {author} {\bibfnamefont {Andrew~M}\ \bibnamefont {Childs}}, \bibinfo {author} {\bibfnamefont {Tongyang}\ \bibnamefont {Li}}, \ and\ \bibinfo {author} {\bibfnamefont {Xiaodi}\ \bibnamefont {Wu}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum algorithms and lower bounds for convex optimization},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Quantum}\ }\textbf {\bibinfo {volume} {4}},\ \bibinfo {pages} {221} (\bibinfo {year} {2020})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Arora}\ \emph {et~al.}(2005)\citenamefont {Arora}, \citenamefont {Hazan},\ and\ \citenamefont {Kale}}]{arora2005fast}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Sanjeev}\ \bibnamefont {Arora}}, \bibinfo {author} {\bibfnamefont {Elad}\ \bibnamefont {Hazan}}, \ and\ \bibinfo {author} {\bibfnamefont {Satyen}\ \bibnamefont {Kale}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Fast algorithms for approximate semidefinite programming using the multiplicative weights update method},}\ }in\ \href@noop {} {\emph {\bibinfo {booktitle} {46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)}}}\ (\bibinfo {organization} {IEEE},\ \bibinfo {year} {2005})\ pp.\ \bibinfo {pages} {339--348}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Van~Apeldoorn}\ \emph {et~al.}(2020)\citenamefont {Van~Apeldoorn}, \citenamefont {Gily{\'e}n}, \citenamefont {Gribling},\ and\ \citenamefont {de~Wolf}}]{van2020quantum}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Joran}\ \bibnamefont {Van~Apeldoorn}}, \bibinfo {author} {\bibfnamefont {Andr{\'a}s}\ \bibnamefont {Gily{\'e}n}}, \bibinfo {author} {\bibfnamefont {Sander}\ \bibnamefont {Gribling}}, \ and\ \bibinfo {author} {\bibfnamefont {Ronald}\ \bibnamefont {de~Wolf}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum {SDP}-solvers: Better upper and lower bounds},}\ }\href {https://doi.org/10.22331/q-2020-02-14-230} {\bibfield  {journal} {\bibinfo  {journal} {Quantum}\ }\textbf {\bibinfo {volume} {4}},\ \bibinfo {pages} {230} (\bibinfo {year} {2020})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {van Apeldoorn}(2020)}]{van2020phd}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Joran}\ \bibnamefont {van Apeldoorn}},\ }\emph {\bibinfo {title} {A quantum view on convex optimization}},\ \href@noop {} {Ph.D. thesis},\ \bibinfo  {school} {University of Amsterdam Institute for Logic, Language and Computation (ILLC)} (\bibinfo {year} {2020})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Jain}\ \emph {et~al.}(2011)\citenamefont {Jain}, \citenamefont {Ji}, \citenamefont {Upadhyay},\ and\ \citenamefont {Watrous}}]{qippspace2011}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Rahul}\ \bibnamefont {Jain}}, \bibinfo {author} {\bibfnamefont {Zhengfeng}\ \bibnamefont {Ji}}, \bibinfo {author} {\bibfnamefont {Sarvagya}\ \bibnamefont {Upadhyay}}, \ and\ \bibinfo {author} {\bibfnamefont {John}\ \bibnamefont {Watrous}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Qip = pspace},}\ }\href {\doibase 10.1145/2049697.2049704} {\bibfield  {journal} {\bibinfo  {journal} {J. ACM}\ }\textbf {\bibinfo {volume} {58}} (\bibinfo {year} {2011}),\ 10.1145/2049697.2049704}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Giovannetti}\ \emph {et~al.}(2008{\natexlab{a}})\citenamefont {Giovannetti}, \citenamefont {Lloyd},\ and\ \citenamefont {Maccone}}]{GLM08a}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Vittorio}\ \bibnamefont {Giovannetti}}, \bibinfo {author} {\bibfnamefont {Seth}\ \bibnamefont {Lloyd}}, \ and\ \bibinfo {author} {\bibfnamefont {Lorenzo}\ \bibnamefont {Maccone}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Quantum random access memory},}\ }\href {\doibase 10.1103/PhysRevLett.100.160501} {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. Lett.}\ }\textbf {\bibinfo {volume} {100}},\ \bibinfo {pages} {160501} (\bibinfo {year} {2008}{\natexlab{a}})},\ \Eprint {http://arxiv.org/abs/0708.1879} {arxiv:0708.1879 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Giovannetti}\ \emph {et~al.}(2008{\natexlab{b}})\citenamefont {Giovannetti}, \citenamefont {Lloyd},\ and\ \citenamefont {Maccone}}]{GLM08}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Vittorio}\ \bibnamefont {Giovannetti}}, \bibinfo {author} {\bibfnamefont {Seth}\ \bibnamefont {Lloyd}}, \ and\ \bibinfo {author} {\bibfnamefont {Lorenzo}\ \bibnamefont {Maccone}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Architectures for a quantum random access memory},}\ }\href {\doibase 10.1103/PhysRevA.78.052310} {\bibfield  {journal} {\bibinfo  {journal} {Phys. Rev. A}\ }\textbf {\bibinfo {volume} {78}},\ \bibinfo {pages} {052310} (\bibinfo {year} {2008}{\natexlab{b}})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Aaronson}(2015)}]{Aar15}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Scott}\ \bibnamefont {Aaronson}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Read the fine print},}\ }\href {\doibase 10.1038/nphys3272} {\bibfield  {journal} {\bibinfo  {journal} {Nature Phys}\ }\textbf {\bibinfo {volume} {11}},\ \bibinfo {pages} {291--293} (\bibinfo {year} {2015})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Di~Matteo}\ \emph {et~al.}(2020)\citenamefont {Di~Matteo}, \citenamefont {Gheorghiu},\ and\ \citenamefont {Mosca}}]{DGM20}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Olivia}\ \bibnamefont {Di~Matteo}}, \bibinfo {author} {\bibfnamefont {Vlad}\ \bibnamefont {Gheorghiu}}, \ and\ \bibinfo {author} {\bibfnamefont {Michele}\ \bibnamefont {Mosca}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Fault tolerant resource estimation of quantum random-access memories},}\ }\href {\doibase 10.1109/TQE.2020.2965803} {\bibfield  {journal} {\bibinfo  {journal} {IEEE Trans. Quantum Eng.}\ }\textbf {\bibinfo {volume} {1}},\ \bibinfo {pages} {1--13} (\bibinfo {year} {2020})},\ \Eprint {http://arxiv.org/abs/1902.01329} {arxiv:1902.01329 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Clader}\ \emph {et~al.}(2022)\citenamefont {Clader}, \citenamefont {Dalzell}, \citenamefont {Stamatopoulos}, \citenamefont {Salton}, \citenamefont {Berta},\ and\ \citenamefont {Zeng}}]{CDS+22}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {B.~David}\ \bibnamefont {Clader}}, \bibinfo {author} {\bibfnamefont {Alexander~M.}\ \bibnamefont {Dalzell}}, \bibinfo {author} {\bibfnamefont {Nikitas}\ \bibnamefont {Stamatopoulos}}, \bibinfo {author} {\bibfnamefont {Grant}\ \bibnamefont {Salton}}, \bibinfo {author} {\bibfnamefont {Mario}\ \bibnamefont {Berta}}, \ and\ \bibinfo {author} {\bibfnamefont {William~J.}\ \bibnamefont {Zeng}},\ }\href {\doibase 10.48550/arXiv.2206.03505} {\enquote {\bibinfo {title} {Quantum {{Resources Required}} to {{Block-Encode}} a {{Matrix}} of {{Classical Data}}},}\ } (\bibinfo {year} {2022}),\ \Eprint {http://arxiv.org/abs/2206.03505} {arxiv:2206.03505 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Jaques}\ and\ \citenamefont {Rattew}(2023)}]{JR23}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Samuel}\ \bibnamefont {Jaques}}\ and\ \bibinfo {author} {\bibfnamefont {Arthur~G.}\ \bibnamefont {Rattew}},\ }\href {\doibase 10.48550/arXiv.2305.10310} {\enquote {\bibinfo {title} {{{QRAM}}: {{A Survey}} and {{Critique}}},}\ } (\bibinfo {year} {2023}),\ \Eprint {http://arxiv.org/abs/2305.10310} {arxiv:2305.10310 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Grigoriadis}\ and\ \citenamefont {Khachiyan}(1991)}]{grigoriadis1991approximate}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Michael~D.}\ \bibnamefont {Grigoriadis}}\ and\ \bibinfo {author} {\bibfnamefont {Leonid~G.}\ \bibnamefont {Khachiyan}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {Approximate solution of matrix games in parallel},}\ }in\ \href@noop {} {\emph {\bibinfo {booktitle} {Advances in Optimization and Parallel Computing}}},\ \bibinfo {editor} {edited by\ \bibinfo {editor} {\bibfnamefont {Panos~M.}\ \bibnamefont {Pardalos}}}\ (\bibinfo {organization} {Elsevier},\ \bibinfo {year} {1991})\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Grigoriadis}\ and\ \citenamefont {Khachiyan}(1995)}]{grigoriadis1995sublinear}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Michael~D.}\ \bibnamefont {Grigoriadis}}\ and\ \bibinfo {author} {\bibfnamefont {Leonid~G.}\ \bibnamefont {Khachiyan}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {A sublinear-time randomized approximation algorithm for matrix games},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Operations Research Letters}\ }\textbf {\bibinfo {volume} {18}},\ \bibinfo {pages} {53--58} (\bibinfo {year} {1995})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Marecek}\ and\ \citenamefont {Akhriev}(2021)}]{marecek2021cuttingplane}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Jakub}\ \bibnamefont {Marecek}}\ and\ \bibinfo {author} {\bibfnamefont {Albert}\ \bibnamefont {Akhriev}},\ }\href@noop {} {\enquote {\bibinfo {title} {A cutting-plane method for semidefinite programming with potential applications on noisy quantum devices},}\ } (\bibinfo {year} {2021}),\ \Eprint {http://arxiv.org/abs/2110.03400} {arXiv:2110.03400 [quant-ph]} \BibitemShut {NoStop}%
\bibitem [{\citenamefont {Chakraborty}\ \emph {et~al.}(2019)\citenamefont {Chakraborty}, \citenamefont {Gily{\'e}n},\ and\ \citenamefont {Jeffery}}]{chakraborty2019power}%
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\bibfield  {author} {\bibinfo {author} {\bibfnamefont {Shantanav}\ \bibnamefont {Chakraborty}}, \bibinfo {author} {\bibfnamefont {Andr{\'a}s}\ \bibnamefont {Gily{\'e}n}}, \ and\ \bibinfo {author} {\bibfnamefont {Stacey}\ \bibnamefont {Jeffery}},\ }\bibfield  {title} {\enquote {\bibinfo {title} {The power of block-encoded matrix powers: Improved regression techniques via faster hamiltonian simulation},}\ }\href@noop {} {\bibfield  {journal} {\bibinfo  {journal} {Leibniz international proceedings in informatics}\ }\textbf {\bibinfo {volume} {132}} (\bibinfo {year} {2019})}\BibitemShut {NoStop}%
\bibitem [{\citenamefont {Rebentrost}\ \emph {et~al.}(2019)\citenamefont {Rebentrost}, \citenamefont {Schuld}, \citenamefont {Wossnig}, \citenamefont {Petruccione},\ and\ \citenamefont {Lloyd}}]{rebentrost2019quantum}%
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