An efficient and exact noncommutative quantum Gibbs sampler

Understand

Preparing thermal and ground states is an essential quantum algorithmic task for quantum simulation.

• In this work, we construct the first efficiently implementable and exactly detailed-balanced Lindbladian for Gibbs states of arbitrary noncommutative Hamiltonians.
• Our construction can also be regarded as a continuous-time quantum analog of the Metropolis-Hastings algorithm.
• To prepare the quantum Gibbs state, our algorithm invokes Hamiltonian simulation for a time proportional to the mixing time and the inverse temperature $\beta$, up to polylogarithmic factors.