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Simulating quantum imaginary-time evolution (QITE) is a major promise of quantum computation.
“Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision”
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W. Fraser · 1965
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M. Abramowitz and I.. Stegun · 1966
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“Reducibility among combinatorial problems”
Richard. Karp · 1972
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“Inequalities for generalized hypergeometric functions”
Yudell Luke · 1972
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“Solvable model of a spin glass”
D. Sherrington and S. Kirkpatrick · 1975
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“Error of truncated Chebyshev series and other near minimax polynomial approximations”
D. Elliott, D.F. Paget, G.M. Phillips and P.J. Taylor · 1987
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“Limit on the Speed of Quantum Computation in Determining Parity”
Edward Farhi, Jeffrey Goldstone, Sam Gutmann and Michael Sipser · 1998
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“Quantum lower bounds by polynomials”
Robert Beals et al · 1998
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“Quantum Computation by Adiabatic Evolution”
Edward Farhi, Jeffrey Goldstone, Sam Gutmann and Michael Sipser · 2000
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“Gadgets, Approximation, and Linear Programming”
Luca Trevisan, Gregory Sorkin, Madhu Sudan and David Williamson · 2000
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“Quantum amplitude amplification and estimation”
Gilles Brassard, Peter Høyer, Michele Mosca and Alain Tapp · 2002
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“Efficient Phase Factor Evaluation in Quantum Signal Processing”, 2020
Yulong Dong, Xiang Meng, K. Whaley and Lin Lin · 2002
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“Finding Angles for Quantum Signal Processing with Machine Precision”, 2020
Rui Chao et al · 2003
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“The Complexity of the Local Hamiltonian Problem”
Julia Kempe, Alexei Kitaev and Oded Regev · 2006
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“Efficient Quantum Algorithms for Simulating Sparse Hamiltonians”
Dominic Berry, Graeme Ahokas, Richard Cleve and Barry Sanders · 2007
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“Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer”
David Poulin and Pawel Wocjan · 2009
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“Adiabatic quantum optimization fails for random instances of NP-complete problems”
Boris Altshuler, Hari Krovi and Jeremie Roland · 2009
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“Preparing thermal states of quantum systems by dimension reduction”
Ersen Bilgin and Sergio Boixo · 2010
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“Anderson localization makes adiabatic quantum optimization fail”
Boris Altshuler, Hari Krovi and Jeremie Roland · 2010
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“Restricted boltzmann machines are hard to approximately evaluate or simulate”
Phillip. Long and Rocco. Servedio · 2010
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“Quantum Metropolis sampling”
K. Temme et al · 2011
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“A quantum–quantum metropolis algorithm”
M.-H. Yung and A. Aspuru-Guzik · 2012
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“The Sherrington-Kirkpatrick model: an overview”
Dmitry Panchenko · 2012
Earlier work this paper cites.
“A quantum approximate optimization algorithm”
E. Farhi, J. Goldstone, S. Gutmann and M. Sipser · 2014
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“A variational eigenvalue solver on a photonic quantum processor”
A. Peruzzo et al · 2014
Cited alongside, same era.
“Exponential improvement in precision for simulating sparse Hamiltonians”
Dominic. Berry et al · 2014
Cited alongside, same era.
“Hamiltonian simulation with nearly optimal dependence on all parameters”
Dominic. Berry, Andrew. Childs and Robin Kothari · 2015
Cited alongside, same era.
“Simulating Hamiltonian Dynamics with a Truncated Taylor Series”
Dominic Berry et al · 2015
Cited alongside, same era.
“Quantum Gibbs Samplers: the commuting case”
Michael. Kastoryano and Fernando… Brandão · 2016
Cited alongside, same era.
“Methodology of Resonant Equiangular Composite Quantum Gates”
Guang Low, Theodore. Yoder and Isaac. Chuang · 2016
Cited alongside, same era.
“Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution”
Mario Motta et al · 2020
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“Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry”
N. Gomes et al · 2020
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“Quantum SDP-Solvers: Better upper and lower bounds”
Joran van Apeldoorn, András Gilyén, Sander Gribling and Ronald de Wolf · 2020
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“Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature”
Tomotaka Kuwahara, Kohtaro Kato and Fernando… Brandão · 2020
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“Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm”
Jessica Lemieux et al · 2020
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“Quantum algorithms for Gibbs sampling and hitting-time estimation”
Anirban Chowdhury and Rolando. Somma · 2017
Cited alongside, same era.
“Quantum SDP Solvers: Large Speed-ups, Optimality, and Applications to Quantum Learning”
Fernando… Brandão et al · 2017
Cited alongside, same era.
“Quantum Speed-ups for SemidefiniteProgramming”
Fernando… Brandão and Krysta. Svore · 2017
Cited alongside, same era.
“Tomography and Generative Data Modeling via Quantum Boltzmann Training”
Maria Kieferova and Nathan Wiebe · 2017
Cited alongside, same era.
“Quantum machine learning”
Jacob nd Peter, Nicola Pancotti, Nathan Patrick and Seth Lloyd · 2017
Cited alongside, same era.
“Optimal Hamiltonian Simulation by Quantum Signal Processing”
Guang Low and Isaac. Chuang · 2017
Cited alongside, same era.
Shi-Ning Sun et al · 2021
Closest in time.
“Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation”
H. Nishi, T. Kosugi and Y Matsushita · 2021
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“Variational Quantum Gibbs State Preparation with a Truncated Taylor Series”
Youle Wang, Guangxi Li and Xin Wang · 2021
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“Computing partition functions in the one clean qubit model”
A.. Chowdhury, R.. Somma and Y. Subasi · 2021
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“Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor”
Matthew. Harrigan et al · 2021
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“Variational Quantum Boltzmann Machines”
Christa Zoufal, Aurélien Lucchi and Stefan Woerner · 2021
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“Hardware-efficient variational quantum algorithms for time evolution”
Marcello Benedetti, Mattia Fiorentini and Michael Lubasch · 2021
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“Real- and Imaginary-Time Evolution with Compressed Quantum Circuits”
Sheng-Hsuan Lin et al · 2021
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“Quantum imaginary time evolution steered by reinforcement learning”, 2021
Chenfeng Cao et al · 2021
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“Resource estimate for quantum many-body ground-state preparation on a quantum computer”
Jessica Lemieux, Guillaume Duclos-Cianci, David Sénéchal and David Poulin · 2021
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“scarrazza/QITE: v1.0.0”
Thais. Silva, Marcio. Taddei, Stefano Carrazza and Leandro Aolita · 2021
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“Hamiltonian singular value transformation and inverse block encoding”
S. Lloyd et al · 2021
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“One qubit as a universal approximant”
Adrián Pérez-Salinas et al · 2021
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“Supplementary material: Fragmented imaginary-time evolution for early-stage quantum signal processors”, 2022
Thais. Silva, Màrcio Taddei, Stefano Carrazza and Leandro Aolita · 2022
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“Fourier-based quantum signal processing”, 2022
Thais. Silva, Lucas Borges and Leandro Aolita · 2022
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“The Quantum Approximate Optimization Algorithm and the Sherrington-Kirkpatrick Model at Infinite Size”
Edward Farhi, Jeffrey Goldstone, Sam Gutmann and Leo Zhou · 2022
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“Low depth algorithms for quantum amplitude estimation”
Tudor Giurgica-Tiron et al · 2022
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“Low-depth amplitude estimation on a trapped-ion quantum computer”
Tudor Giurgica-Tiron et al · 2022
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In in preparation , 2023
Lucas Borges, Giancarlo Camilo, Thais. Silva and Leandro Aolita · 2023
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