Stoquastic simulations of non-stoquastic superconducting flux circuits

Abstract There is a tremendous interest in fabricating superconducting flux circuits that are non-stoquastic-i.e., have positive off-diagonal matrix elements-in their qubit representation, as these circuits are thought to evade sign-problem-free Quantum Monte Carlo (QMC) approaches and could play a key role in the demonstration of speedups in quantum annealing protocols. We show, however, that for a broad class of such flux circuits, with a positive quadratic charge sector and a flux-dependent potential, direct simulation of the underlying continuous-variable circuit Hamiltonian yields a sign-problem-free QMC representation. Our approach not only obviates the reduction of flux circuits to their qubit representation, but also produces results that are more directly tied to the experimental degrees of freedom. We discuss the implications of our work, arguing that apparent non-stoquasticity in the effective qubit description does not necessarily imply non-stoquasticity, or a QMC sign problem, at the circuit level. These findings call for a careful reassessment of attempts to engineer non-stoquasticity in superconducting flux-based quantum annealers in pursuit of universality.