Quantum Thermal State Preparation

TL;DR

This paper introduces efficient quantum algorithms for preparing thermal states and Gibbs states, overcoming previous obstacles and providing rigorous proofs of thermalization, with potential significant impact on quantum simulation and thermodynamics.

Contribution

It presents simple continuous-time quantum Gibbs samplers that overcome energy-time uncertainty issues and introduces the first provably accurate algorithm for certain purified Gibbs states, with quantum speedup.

Findings

Algorithms have provable dependence on temperature, accuracy, and spectral gap.

First rigorous proof of finite-time thermalization for physically derived Lindbladians.

Quantum Gibbs sampling is poised to become essential in quantum computing.

Abstract

Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged. Monte Carlo-style quantum Gibbs samplers have emerged as an alternative, but prior proposals have been unsatisfactory due to technical obstacles rooted in energy-time uncertainty. We introduce simple continuous-time quantum Gibbs samplers that overcome these obstacles by efficiently simulating Nature-inspired quantum master equations (Lindbladians). In addition, we construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states (called thermal field double states in high-energy physics) of rapidly thermalizing systems; this algorithm also benefits from a quantum walk speedup. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time (or spectral gap) of the relevant Lindbladian. We complete the first rigorous proof of finite-time thermalization for physically derived Lindbladians by developing a general analytic framework for nonasymptotic secular approximation and approximate detailed balance. Given the success of classical Markov chain Monte Carlo (MCMC) algorithms and the ubiquity of thermodynamics, we anticipate that quantum Gibbs sampling will become indispensable in quantum computing.