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Path integral quantum Monte Carlo (PIMC) is a method for estimating thermal equilibrium properties of stoquastic quantum spin systems by sampling from a classical Gibbs distribution using Markov chain Monte Carlo.
Maximum properties and inequalities for the eigenvalues of completely continuous operators
Ky Fan · 1951
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Probability inequalities for sums of bounded random variables
Wassily Hoeffding · 1963
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Monte Carlo simulation of quantum spin systems
Masuo Suzuki, Seiji Miyashita, and Akira Kuroda · 1977
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Quantum statistical Monte Carlo methods and applications to spin systems
Masuo Suzuki · 1986
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Polynomial-time approximation algorithms for the Ising model
Mark Jerrum and Alistair Sinclair · 1993
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The Markov chain Monte Carlo method: An approach to approximate counting and integration
Mark Jerrum and Alistair Sinclair · 1997
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Quantum annealing in the transverse Ising model
Tadashi Kadowaki and Hidetoshi Nishimori · 1998
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Stochastic series expansion method with operator-loop update
Anders W Sandvik · 1999
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A quantum adiabatic evolution algorithm applied to random instances of an np-complete problem
Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Joshua Lapan, Andrew Lundgren, and Daniel Preda · 2001
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Quantum monte carlo simulations of solids
WMC Foulkes, L Mitas, RJ Needs, and G Rajagopal · 2001
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Quantum adiabatic evolution algorithms versus simulated annealing, 2002, arXiv:quant-ph/0201031
Edward Farhi, Jeffrey Goldstone, and Sam Gutmann · 2002
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Quantum annealing by the path-integral monte carlo method: The two-dimensional random ising model
Roman Martonák, Giuseppe E. Santoro, and Erio Tosatti · 2002
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The quantum adiabatic optimization algorithm and local minima
Ben W Reichardt · 2004
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The complexity of stoquastic local Hamiltonian problems
Sergey Bravyi, David P. DiVincenzo, Roberto I. Oliveira, and Barbara M. Terhal · 2006
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Quantum annealing of an Ising spin-glass by Green’s function Monte Carlo
Lorenzo Stella and Giuseppe E Santoro · 2007
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Accelerating simulated annealing for the permanent and combinatorial counting problems
Ivona Bezáková, Daniel Štefankovič, Vijay V. Vazirani, and Eric Vigoda · 2008
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Markov Chains and Mixing Times
D.A. Levin, Y. Peres, and E.L. Wilmer · 2008
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Frank Verstraete, Valentin Murg, and J Ignacio Cirac · 2008
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Complexity of stoquastic frustration-free Hamiltonians
Sergey Bravyi and Barbara M. Terhal · 2009
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Quantum adiabatic computation with a constant gap is not useful in one dimension
M. B. Hastings · 2009
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Tunneling and speedup in quantum optimization for permutation-symmetric problems
Siddharth Muthukrishnan, Tameem Albash, and Daniel A Lidar · 2016
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Off-diagonal expansion quantum monte carlo
Tameem Albash, Gene Wagenbreth, and Itay Hen · 2017
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Can quantum Monte Carlo simulate quantum annealing?, 2017, arXiv:1703.09277
Evgeny Andriyash and Mohammad H Amin · 2017
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Rigorous RG algorithms and area laws for low energy eigenstates in 1D
Itai Arad, Zeph Landau, Umesh Vazirani, and Thomas Vidick · 2017
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Polynomial-time classical simulation of quantum ferromagnets
Sergey Bravyi and David Gosset · 2017
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Alessandra Cipriani and Paolo Dai Pra · 2010
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Glauber dynamics for the quantum Ising model in a transverse field on a regular tree
Fabio Martinelli and Marc Wouts · 2012
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Obstructions to classically simulating the quantum adiabatic algorithm
Matthew B Hastings and MH Freedman · 2013
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A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
Zeph Landau, Umesh Vazirani, and Thomas Vidick · 2013
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Quantum Ising Phases and Transitions in Transverse Ising Models
S. Suzuki, J. Inoue, and B.K. Chakrabarti · 2013
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Different strategies for optimization using the quantum adiabatic algorithm, 2014, arXiv:1401.7320
Elizabeth Crosson, Edward Farhi, Cedric Yen-Yu Lin, Han-Hsuan Lin, and Peter Shor · 2014
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Monte Carlo simulation of stoquastic Hamiltonians
Sergey Bravyi · 2015
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Sergey Bravyi and Matthew Hastings · 2017
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Nonstoquastic hamiltonians and quantum annealing of an ising spin glass
Layla Hormozi, Ethan W. Brown, Giuseppe Carleo, and Matthias Troyer · 2017
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Substochastic Monte Carlo algorithms, 2017, arXiv:1704.09014
Michael Jarret and Brad Lackey · 2017
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Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations
Zhang Jiang, Vadim N Smelyanskiy, Sergei V Isakov, Sergio Boixo, Guglielmo Mazzola, Matthias Troyer, and Hartmut Neven · 2017
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Non-stoquastic hamiltonians in quantum annealing via geometric phases
Walter Vinci and Daniel A Lidar · 2017
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Adiabatic quantum computation
Tameem Albash and Daniel A. Lidar · 2018
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Diffusion monte carlo approach versus adiabatic computation for local hamiltonians
Jacob Bringewatt, William Dorland, Stephen P. Jordan, and Alan Mink · 2018
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Universal quantum hamiltonians
Toby S. Cubitt, Ashley Montanaro, and Stephen Piddock · 2018
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Exponential speedup of quantum annealing by inhomogeneous driving of the transverse field
Yuki Susa, Yu Yamashiro, Masayuki Yamamoto, and Hidetoshi Nishimori · 2018
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