Quantum Gibbs Sampling

Author: Chen, Chi-Fang

Year: 2025

Degree: Dissertation (Ph.D.)

Advisor: Brandao, Fernando

Committee Members: Preskill, John P.; Motrunich, Olexei I.; Tropp, Joel A.; Brandao, Fernando

Option: Physics

DOI: 10.7907/dy0f-3216

Abstract

Markov Chain Monte Carlo algorithms are indispensable in classical thermodynamic simulation, perhaps due to their mathematical simplicity, algorithmic efficiency, and physical origin. In particular, Glauber dynamics is a detailed-balanced continuous-time Markov chain that fixes the Gibbs distribution and also serves as a mathematically succinct model of classical thermalization. In this thesis, we proposed a quantum computation analog of Glauber dynamics that is exactly detailed balanced yet algorithmic efficient, inherits the locality of the target Hamiltonian, and resembles Davies'-like generators physically derived from a weak system-bath coupling. We hope our proposal will serve as a quantum algorithm for quantum thermodynamic simulation and a model of open system thermalization where a suitable construction has been lacking for noncommuting Hamiltonians.

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