Mixing time of quantum Gibbs sampling for random sparse Hamiltonians

Understand

Providing evidence that quantum computers can efficiently prepare low-energy or thermal states of physically relevant interacting quantum systems is a major challenge in quantum information science.

• A newly developed quantum Gibbs sampling algorithm by Chen, Kastoryano, and Gily\'en provides an efficient simulation of the detailed-balanced dissipative dynamics of non-commutative quantum systems.
• The running time of this algorithm depends on the mixing time of the corresponding quantum Markov chain, which has not been rigorously bounded except in the high-temperature regime.
• In this work, we establish a polylog(n) upper bound on its mixing time for various families of random n by n sparse Hamiltonians at any constant temperature.