Efficient Algorithms for Approximating Quantum Partition Functions at Low Temperature

Tyler Helmuth1 and Ryan L. Mann2,3

1Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, United Kingdom
2Centre for Quantum Computation and Communication Technology, Centre for Quantum Software and Information, School of Computer Science, Faculty of Engineering & Information Technology, University of Technology Sydney, NSW 2007, Australia
3School of Mathematics, University of Bristol, Bristol, BS8 1UG, United Kingdom

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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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Cited by

[1] Ryan L. Mann and Romy M. Minko, "Algorithmic Cluster Expansions for Quantum Problems", PRX Quantum 5 1, 010305 (2024).

[2] Álvaro M. Alhambra, "Quantum Many-Body Systems in Thermal Equilibrium", PRX Quantum 4 4, 040201 (2023).

[3] Viresh Patel and Guus Regts, "Approximate counting using Taylor's theorem: a survey", arXiv:2212.08143, (2022).

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