Journal Article
Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature
Tyler Helmuth,Ryan Mann +1 more
TL;DR: An efficient approximation algorithm is established for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems.
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Abstract: We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on combining the contour representation of quantum spin systems of this type due to Borgs, Kotecký, and Ueltschi with the algorithmic framework developed by Helmuth, Perkins, and Regts, and Borgs et al.
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Citations
Peer Review
Approximate counting using Taylor’s theorem
Viresh Patel,Guus Regts +1 more
TL;DR: Barvinok et al. as discussed by the authors proposed a new algorithm based on Taylor's theorem for computing the permanent of certain matrices, and the approach has been applied to various graph polynomials.
Approximate counting using Taylor's theorem: a survey
Vir D. Patel,Guus Regts +1 more
TL;DR: In this paper , the authors propose a solution to solve the problem of the problem: this paper ] of "uniformity" and "uncertainty" of the solution.
Algorithmic Cluster Expansions for Quantum Problems
Ryan Mann,Romy Minko +1 more
TL;DR: In this paper , the authors established a general framework for computing approximation algorithms for counting problems based on the cluster expansion of abstract polymer models formalism of Kotecky and Preiss, and applied their framework to obtain efficient algorithms for approximating probability amplitudes of a class of quantum circuits close to the identity.
Peer Review
Quantum many-body systems in thermal equilibrium
'Alvaro M. Alhambra
- 18 Apr 2022
TL;DR: In this paper , the authors give a pedagogical overview of some of the most important universal features about the physics and complexity of these states, which have the locality of the Hamiltonian at its core.
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TL;DR: A randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic Ising system to any specified degree of accuracy is presented.
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TL;DR: It is shown that on any graph of maximum degree Δ correlations decay with distance at least as fast as they do on the regular tree of the same degree, which resolves an open conjecture in statistical physics.
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TL;DR: In this paper, the authors give a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kac interactions.
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