Quantum Markov chain Monte Carlo with programmable quantum simulators

Abstract: In this work, we present a quantum Markov chain algorithm for many-body systems that utilizes a special phase of matter known as the Many-Body Localized (MBL) phase. We show how the properties of the MBL phase enable one to address the conditions for ergodicity and sampling from distributions of quantum states. We demonstrate how to exploit the thermalized-to-localized transition to tune the acceptance rate of the Markov chain, and apply the algorithm to solve a range of combinatorial optimization problems of quadratic order and higher. The algorithm can be implemented on any quantum hardware capable of simulating the Floquet dynamics of a 1D Ising chain with nearest-neighbor interactions, providing a practical way of extending the range of simulable Hamiltonians of current QPUs.