Efficient Algorithms for Approximating Quantum Partition Functions

Ryan L. Mann; Tyler Helmuth

doi:10.1063/5.0013689

Efficient Algorithms for Approximating Quantum Partition Functions

Ryan L. Mann^*, Tyler Helmuth

^*Corresponding author for this work

School of Mathematics

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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
Article number	022201
Number of pages	8
Journal	Journal of Mathematical Physics
Volume	62
Issue number	2
Early online date	1 Feb 2021
DOIs	https://doi.org/10.1063/5.0013689
Publication status	Published - 1 Feb 2021

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Montanaro, A. M. R.
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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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AB - 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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M3 - Article (Academic Journal)

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Efficient Algorithms for Approximating Quantum Partition Functions

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