Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical system into an ensemble to recover a probability distribution. At a critical constraint to variable ratio, decision problems$-$such as propositional satisfiability$-$appear to statistically exhibit an abrupt transition in required computational resources. This so called, algorithmic or computational phase transition signature, has yet-to-be observed in contemporary physics based processors. We found that the computational phase transition admits a signature in Gibbs' distributions and hence we predict and prescribe the physical observation of this effect. We simulate such an experiment, that when realized experimentally, we believe would represent a milestone in the physical theory of computation.
Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians
Joint Center for Quantum Information & Computer Science, National Institute of Standards & Technology and University of Maryland, College Park（量子信息与计算联合中心，美国国家标准与技术研究院和马里兰大学帕克分校）；Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park（计算机科学系和高级计算机研究所，马里兰大学帕克分校）
Polynomial-time thermalization and Gibbs sampling from system-bath couplings
Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP（里昂大学，巴黎高等师范学院里昂分校，里昂第一大学，法国国家科学研究中心，法国信息与自动化研究所，里昂理工学院）；Instituto de Física Téorica UAM/CSIC（马德里自治大学/西班牙国家研究委员会理论物理研究所）；Department of Mathematical Sciences, University of Copenhagen（哥本哈根大学数学科学系）；Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris（法国信息与自动化研究所，巴黎电信学院通信与图像处理实验室，巴黎理工学院）
Gibbs state preparation for commuting Hamiltonian: Mapping to classical Gibbs sampling
School of Engineering and Applied Sciences, Harvard University（哈佛大学工程与应用科学学院）；Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）；Simons Institute for the Theory of Computing, University of California, Berkeley（加州大学伯克利分校西蒙斯计算理论研究所）
An (almost) efficient classical algorithm for sampling from typical Gibbs states
Institute for Quantum Information and Matter, Caltech（加州理工学院量子信息与物质研究所）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Department of Computer Science, National University of Singapore（新加坡国立大学计算机科学系）；Walter Burke Institute for Theoretical Physics, Caltech（加州理工学院沃尔特·伯克理论物理研究所）
Computing the free energy of quantum Coulomb gases and molecules via quantum Gibbs sampling
Uni Bocconi（博科尼大学）；Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎高等电信学校-通信与图像处理实验室，巴黎理工学院）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）
Classical Estimation of the Free Energy and Quantum Gibbs Sampling from the Markov Entropy Decomposition
University of Cambridge（剑桥大学）；Universität Tübingen（蒂宾根大学）；IBM Quantum, IBM T. J. Watson Research Center（IBM量子，IBM T.J.沃森研究中心）；Inria, ENS Lyon, UCBL, LIP（法国国家信息与自动化研究所，里昂高等师范学院，里昂第一大学，计算与并行实验室）；UC Davis（加州大学戴维斯分校）；University of Sydney（悉尼大学）
Accelerating quantum Gibbs sampling without quantum walks
Virginia Tech（弗吉尼亚理工大学）；Simons Institute for the Theory of Computing, University of California, Berkeley（加州大学伯克利分校西蒙斯理论计算研究所）；Department of Mathematics, University of California, Berkeley（加州大学伯克利分校数学系）；Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Thermal expectation estimation via single-trajectory Gibbs sampling with non-destructive measurements
Stanford University（斯坦福大学）；University of California, Berkeley（加州大学伯克利分校）；City University of Hong Kong（香港城市大学）；Institute for Computational and Mathematical Engineering, Stanford University（斯坦福大学计算与数学工程研究所）
Provable Quantum-Classical Separation for Continuous Gibbs Sampling
Irréversible Inc.（不可逆公司）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；National Research Council Canada（加拿大国家研究委员会）
Quasi-optimal sampling from Gibbs states via non-commutative optimal transport metrics
Fachbereich Mathematik, Universität Tübingen（蒂宾根大学数学系）；Dep. of App. Mathematics and Theo. Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Inria, Télécom Paris - LTCI, Institut Polytechnique de Paris（巴黎理工学院电信学院LTCI实验室法国国家信息与自动化研究所）
Quantum Gibbs Sampling in Infinite Dimensions: Generation, Mixing Times and Circuit Implementation
Bocconi University（博科尼大学）；Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎电信学院-通信与图像处理实验室，巴黎理工学院）；Institute for Quantum Information, RWTH Aachen University（亚琛工业大学量子信息研究所）；Inria, ENS de Lyon, Université Claude Bernard Lyon 1, LIP（法国国家信息与自动化研究所，里昂高等师范学校，克劳德·贝尔纳里昂第一大学，计算与信息科学实验室）
