Validating a Two Qubit Non-Stoquastic Hamiltonian in Quantum Annealing

Abstract

We propose a two qubit experiment for validating tunable antiferromagnetic $XX$ interactions in quantum annealing. Such interactions allow the time-dependent Hamiltonian to be non-stoquastic, and the instantaneous ground state can have negative amplitudes in the computational basis. Our construction relies on how the degeneracy of the Ising Hamiltonian's ground states is broken away from the end point of the anneal: above a certain value of the antiferromagnetic $XX$ interaction strength, the perturbative ground state at the end of the anneal changes from a symmetric to an antisymmetric state. This change is associated with a suppression of one of the Ising ground states, which can then be detected using solely computational basis measurements. We show that a semiclassical approximation of the annealing protocol fails to reproduce this feature, making it a candidate `quantum signature' of the evolution.