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Learning the Hamiltonian underlying a quantum many-body system in thermal equilibrium is a fundamental task in quantum learning theory and experimental sciences.
Theory of superconductivity
J. Bardeen, L. N. Cooper, and J. R. Schrieffer · 1957
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Anomalous quantum hall effect: An incompressible quantum fluid with fractionally charged excitations
R. B. Laughlin · 1983
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Quantum metropolis sampling
Kristan Temme, Tobias J Osborne, Karl G Vollbrecht, David Poulin, and Frank Verstraete · 2011
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The sherrington-kirkpatrick model: An overview
Dmitry Panchenko · 2012
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A quantum–quantum Metropolis algorithm
Man-Hong Yung and Alán Aspuru-Guzik · 2012
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Complex-time singularity and locality estimates for quantum lattice systems
Gabriel Bouch · 2015
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Computational implications of reducing data to sufficient statistics, 2015
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Adam Klivans and Raghu Meka · 2017
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Optimal hamiltonian simulation by quantum signal processing
Guang Hao Low and Isaac L Chuang · 2017
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Learning a local hamiltonian from local measurements
Eyal Bairey, Itai Arad, and Netanel H. Lindner · 2019
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Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics
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Sample-efficient learning of quantum many-body systems
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Yotam Y. Lifshitz, Eyal Bairey, Eli Arbel, Gadi Aleksandrowicz, Haggai Landa, and Itai Arad · 2023
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Thermal state preparation via rounding promises
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Szegedy walk unitaries for quantum maps
Pawel Wocjan and Kristan Temme · 2023
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Learning quantum hamiltonians at any temperature in polynomial time
Ainesh Bakshi, Allen Liu, Ankur Moitra, and Ewin Tang · 2024
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Single-ancilla ground state preparation via Lindbladians
Zhiyan Ding, Chi-Fang Chen, and Lin Lin · 2024
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Efficient quantum Gibbs samplers with Kubo–Martin–Schwinger detailed balance condition
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Optimal learning of quantum hamiltonians from high-temperature gibbs states
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Hsin-Yuan Huang, Yu Tong, Di Fang, and Yuan Su · 2023
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Quantum gibbs states are locally markovian
Chi-Fang Chen and Cambyse Rouzé
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Zhiyan Ding, Bowen Li, and Lin Lin · 2024
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Quantum generalizations of glauber and metropolis dynamics
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Quantum Metropolis Sampling via Weak Measurement
Jiaqing Jiang and Sandy Irani · 2024
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Improved algorithms for learning quantum hamiltonians, via flat polynomials
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Learning quantum many-body systems from a few copies
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Hamiltonian and liouvillian learning in weakly-dissipative quantum many-body systems
Tobias Olsacher, Tristan Kraft, Christian Kokail, Barbara Kraus, and Peter Zoller · 2025
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