Efficient Algorithms for Approximating Quantum Partition Functions

Ryan L. Mann; Tyler Helmuth

Efficient Algorithms for Approximating Quantum Partition Functions

Ryan L. Mann, Tyler Helmuth

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal)

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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 Neto\v{c}n\`y 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.

Original language	English
Number of pages	6
Journal	arXiv
Publication status	Unpublished - 24 Apr 2020

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https://arxiv.org/abs/2004.11568

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title = "Efficient Algorithms for Approximating Quantum Partition Functions",

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 Neto\v{c}n\`y 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. ",

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