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We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance.
1906
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1908
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1910
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Huzihiro Araki, “ Gibbs states of a one dimensional quantum lattice
1969
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John M Hammersley and Peter Clifford, “ Markov fields on finite graphs and lattices
1971
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Leonard Gross, “ Decay of correlations in classical lattice models at high temperature
1979
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Robert B. Israel and Chiara R. Nappi, “ Exponential clustering for long-range integer-spin systems
1979
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Camillo Cammarota, “ Decay of correlations for infinite range interactions in unbounded spin systems
1982
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F Barahona, “ On the computational complexity of Ising spin glass models
1982
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Dénes Petz, “ Sufficient subalgebras and the relative entropy of states of a von Neumann algebra
1986
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Yong Moon Park and Hyun Jae Yoo, “ Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems
1995
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Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter, “ Elementary gates for quantum computation
1995
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Herbert Spohn and Wilhelm Zwerger, “ Decay of the Two-Point Function in One-Dimensional O(N) Spin Models with Long-Range Interactions
1999
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Robert Raussendorf and Hans J. Briegel, “ A One-Way Quantum Computer
2001
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Aldo Procacci and Benedetto Scoppola, “ On Decay of Correlations for Unbounded Spin Systems with Arbitrary Boundary Conditions
2001
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W. M. C. Foulkes, L. Mitas, R. J. Needs, and G. Rajagopal, “ Quantum Monte Carlo simulations of solids
2001
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Daniel Ueltschi, “ Cluster expansions and correlation functions
2004
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Juha J. Vartiainen, Mikko Möttönen, and Martti M. Salomaa, “ Efficient Decomposition of Quantum Gates
2004
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F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, “ Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
2004
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Alina Kargol, “ Decay of correlations in multicomponent ferromagnets with long-range interaction
2005
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Sandu Popescu, Anthony J Short, and Andreas Winter, “ Entanglement and the foundations of statistical mechanics
2006
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M. B. Hastings, “ Solving gapped Hamiltonians locally
2006
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Alexei Kitaev and John Preskill, “ Topological Entanglement Entropy
2006
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Michael Levin and Xiao-Gang Wen, “ Detecting Topological Order in a Ground State Wave Function
2006
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Dror Weitz, “ Counting Independent Sets up to the Tree Threshold
2006
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Marcos Rigol, Tyler Bryant, and Rajiv R. P. Singh, “ Numerical Linked-Cluster Approach to Quantum Lattice Models
2006
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D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “ Matrix Product State Representations
2007
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M. B. Hastings, “ Entropy and entanglement in quantum ground states
2007
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Norbert Schuch, Michael M. Wolf, Frank Verstraete, and J. Ignacio Cirac, “ Computational Complexity of Projected Entangled Pair States
2007
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Michael M. Wolf, Frank Verstraete, Matthew B. Hastings, and J. Ignacio Cirac, “ Area Laws in Quantum Systems: Mutual Information and Correlations
2008
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David Poulin and Pawel Wocjan, “ Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer
2009
Cited alongside, same era.
Steven R. White, “ Minimally Entangled Typical Quantum States at Finite Temperature
2009
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Ersen Bilgin and Sergio Boixo, “ Preparing Thermal States of Quantum Systems by Dimension Reduction
2010
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Ersen Bilgin and David Poulin, “ Coarse-grained belief propagation for simulation of interacting quantum systems at all temperatures
2010
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Matthew B. Hastings, “ Topological Order at Nonzero Temperature
2011
Cited alongside, same era.
David Poulin and Matthew B. Hastings, “ Markov Entropy Decomposition: A Variational Dual for Quantum Belief Propagation
Mark M. Wilde, “ Recoverability in quantum information theory
2015
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Benjamin J. Brown, Daniel Loss, Jiannis K. Pachos, Chris N. Self, and James R. Wootton, “ Quantum memories at finite temperature
2016
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2016
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Liujun Zou and Jeongwan Haah, “ Spurious long-range entanglement and replica correlation length
2016
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David Sutter, Omar Fawzi, and Renato Renner, “ Universal recovery map for approximate Markov chains
2016
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2011
Cited alongside, same era.
Tobias J Osborne, “ Hamiltonian complexity
2012
Cited alongside, same era.
Winton Brown and David Poulin, “ Quantum Markov networks and commuting Hamiltonians
2012
Cited alongside, same era.
Alistair Sinclair, Piyush Srivastava, and Marc Thurley, “ Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs
2012
Cited alongside, same era.
Thomas Koffel, M. Lewenstein, and Luca Tagliacozzo, “ Entanglement Entropy for the Long-Range Ising Chain in a Transverse Field
2012
Cited alongside, same era.
Olivier Landon-Cardinal and David Poulin, “ Local Topological Order Inhibits Thermal Stability in 2D
2013
Cited alongside, same era.
Sergey Bravyi and Jeongwan Haah, “ Quantum Self-Correction in the 3D Cubic Code Model
2013
Cited alongside, same era.
2016
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Michael J. Kastoryano and Fernando G. S. L. Brandão, “ Quantum Gibbs Samplers: The Commuting Case
2016
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Yimin Ge, András Molnár, and J. Ignacio Cirac, “ Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States
2016
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Tomotaka Kuwahara, “ Exponential bound on information spreading induced by quantum many-body dynamics with long-range interactions
2016
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Anurag Anshu, Itai Arad, and Aditya Jain, “ How local is the information in tensor networks of matrix product states or projected entangled pairs states
2016
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F. G. S. L. Brandão and K. M. Svore, “ Quantum Speed-Ups for Solving Semidefinite Programs
2017
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J. Van Apeldoorn, A. Gilyén, S. Gribling, and R. de Wolf, “ Quantum SDP-Solvers: Better Upper and Lower Bounds
2017
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Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “ Quantum machine learning
2017
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Mária Kieferová and Nathan Wiebe, “ Tomography and generative training with quantum Boltzmann machines
2017
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J. Liu, A. Sinclair, and P. Srivastava, “ The Ising Partition Function: Zeros and Deterministic Approximation
2017
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Jiehang Zhang, Guido Pagano, Paul W Hess, Antonis Kyprianidis, Patrick Becker, Harvey Kaplan, Alexey V Gorshkov, Z-X Gong, and Christopher Monroe, “ Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator
2017
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Tomotaka Kuwahara, Itai Arad, Luigi Amico, and Vlatko Vedral, “ Local reversibility and entanglement structure of many-body ground states
2017
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Senaida Hernández-Santana, Christian Gogolin, J. Ignacio Cirac, and Antonio Acín, “ Correlation Decay in Fermionic Lattice Systems with Power-Law Interactions at Nonzero Temperature
2017
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M. Schwarz, O. Buerschaper, and J. Eisert, “ Approximating local observables on projected entangled pair states
2017
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Hal Tasaki, “ On the Local Equivalence Between the Canonical and the Microcanonical Ensembles for Quantum Spin Systems
2018
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Mohammad H. Amin, Evgeny Andriyash, Jason Rolfe, Bohdan Kulchytskyy, and Roger Melko, “ Quantum Boltzmann Machine
2018
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David Sutter and Renato Renner, “ Necessary Criterion for Approximate Recoverability
2018
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Marius Junge, Renato Renner, David Sutter, Mark M. Wilde, and Andreas Winter, “ Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy
2018
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Hai-Jing Song, Tieling Song, Qi-Kai He, Yang Liu, and D. L. Zhou, “ Geometry and symmetry in the quantum Boltzmann machine
2019
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Kohtaro Kato and Fernando G. S. L. Brandão, “ Quantum Approximate Markov Chains are Thermal
2019
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Fernando G. S. L. Brandão and Michael J. Kastoryano, “ Finite Correlation Length Implies Efficient Preparation of Quantum Thermal States
2019
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Dominic J. Williamson, Arpit Dua, and Meng Cheng, “ Spurious Topological Entanglement Entropy from Subsystem Symmetries
2019
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Michael J. Kastoryano, Angelo Lucia, and David Perez-Garcia, “ Locality at the Boundary Implies Gap in the Bulk for 2D PEPS
2019
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Tomotaka Kuwahara and Keiji Saito, “ Eigenstate Thermalization from the Clustering Property of Correlation
2020
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Jonas Haferkamp, Dominik Hangleiter, Jens Eisert, and Marek Gluza, “ Contracting projected entangled pair states is average-case hard
2020
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