Thermal State Preparation via Rounding Promises

Patrick Rall1, Chunhao Wang2, and Pawel Wocjan3

1IBM Quantum, MIT-IBM Watson AI Lab, Cambridge, Massachusetts 02142, USA
2Department of Computer Science and Engineering, Pennsylvania State University
3IBM Quantum, Thomas J Watson Research Center, Yorktown Heights, New York 10598, USA

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A promising avenue for the preparation of Gibbs states on a quantum computer is to simulate the physical thermalization process. The Davies generator describes the dynamics of an open quantum system that is in contact with a heat bath. Crucially, it does not require simulation of the heat bath itself, only the system we hope to thermalize. Using the state-of-the-art techniques for quantum simulation of the Lindblad equation, we devise a technique for the preparation of Gibbs states via thermalization as specified by the Davies generator.
In doing so, we encounter a severe technical challenge: implementation of the Davies generator demands the ability to estimate the energy of the system unambiguously. That is, each energy of the system must be deterministically mapped to a unique estimate. Previous work showed that this is only possible if the system satisfies an unphysical 'rounding promise' assumption. We solve this problem by engineering a random ensemble of rounding promises that simultaneously solves three problems: First, each rounding promise admits preparation of a 'promised' thermal state via a Davies generator. Second, these Davies generators have a similar mixing time as the ideal Davies generator. Third, the average of these promised thermal states approximates the ideal thermal state.

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Cited by

[1] Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão, "Quantum algorithms: A survey of applications and end-to-end complexities", arXiv:2310.03011, (2023).

[2] Chi-Fang Chen, Hsin-Yuan Huang, John Preskill, and Leo Zhou, "Local minima in quantum systems", arXiv:2309.16596, (2023).

[3] Mirko Consiglio, "Variational Quantum Algorithms for Gibbs State Preparation", arXiv:2305.17713, (2023).

[4] Xiantao Li and Chunhao Wang, "Simulating Markovian open quantum systems using higher-order series expansion", arXiv:2212.02051, (2022).

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