Efficient Algorithms for Approximating Quantum Partition Functions

2020/04/30 by Ryan L. Mann, Tyler Helmuth · 1 voice
Computer Science · Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Quantum Computing Algorithms and Architecture #Quantum many-body systems #cs.CC #cs.DS #math.CO #quant-ph

paper · pdf · doi:10.1063/5.0013689

published as Journal of Mathematical Physics 62, 022201 (2021) · 7 pages, 0 figures, published version

arxiv created 2021/02/01 · openalex publication_date 2021/02/01 · arxiv updated 2021/02/02 · openalex created_date 2021/02/15 · openalex updated_date 2026/07/28

Abstract

We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Netočný and Redig and the cluster expansion approach to designing algorithms due to Helmuth, Perkins, and Regts. Similar results have previously been obtained by related methods, and our main contribution is a simple and slightly sharper analysis for the case of pairwise interactions on bounded-degree graphs.

Citations

• Classical Simulation of High Temperature Quantum Ising Models
• Efficient algorithms for the Potts model on small-set expanders

Discussions

• I'm pleased that Tyler Helmuth and my paper on efficient algorithms for approximating quantum partition functions was published in the Journal of Mathematical Physics today. https://doi.org/10.1063/5 [bsky, 0 points, 0 comments]

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