Sankara Sai Chaithanya Rayudu

The Quantum Monte Carlo (QMC) method with operator-loop update is a powerful technique that has been extensively used in condensed matter physics. Despite its practical success, no rigorous proof of polynomial-time mixing had been known. In this work, we prove that the operator-loop QMC algorithm applied to all stoquastic (sign-problem free) XY models mixes in time polynomial in the system size and inverse temperature. Our work gives the first polynomial-time algorithm for computing the partition function of all stoquastic XY models. As a consequence, we obtain the first proof that the corresponding ground-state energy estimation problems lie in BPP. Finally, we discuss how operator-loop QMC is empirically known to mix rapidly for an even broader class of stoquastic Hamiltonians, and comment on the physical implications of our proof.