Stoquasticity in circuit QED

TL;DR

This paper investigates the stoquasticity of circuit-QED Hamiltonians, demonstrating conditions under which sign-problem free simulations are possible and how effective non-stoquastic Hamiltonians can arise.

Contribution

It shows that scalable sign-problem free path integral Monte Carlo simulations are generally feasible for coupled flux qubits and clarifies when non-stoquasticity appears or can be avoided.

Findings

Sign-problem free simulations are typically possible for coupled flux qubits.

Non-stoquastic effective Hamiltonians can emerge in certain regimes.

Canonical transformations can prevent non-stoquasticity when capacitive coupling is small.

Abstract

We analyze whether circuit-QED Hamiltonians are stoquastic focusing on systems of coupled flux qubits: we show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. Despite this, we corroborate the recent finding [arXiv:1903.06139] that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits. We find that if the capacitive coupling is sufficiently small, this non-stoquasticity of the effective qubit Hamiltonian can be avoided if we perform a canonical transformation prior to projecting onto an effective qubit Hamiltonian. Our results shed light on the power of circuit-QED Hamiltonians for the use of quantum adiabatic computation and the subtlety of finding a representation which cures the sign problem in these systems