Quantum annealing with error mitigation

Quantum annealing (QA) is one of the efficient methods to calculate the ground state energy of a problem Hamiltonian. If an adiabatic condition is satisfied, we can accurately estimate the ground state energy by using QA without noise. However, in actual physical implementation, systems suffer from decoherence. On the other hand, much effort has been paid into the noisy intermediate-scale quantum (NISQ) computation research. For practical NISQ computation, many error mitigation (EM) methods have been devised to remove noise effects. Here, we propose a QA strategy combined with the EM method called dual-state purification to suppress the effects of decoherence. Our protocol consists of four parts; conventional dynamics, single-qubit projective measurements, Hamiltonian dynamics corresponding to an inverse map of the first dynamics, and post-processing measurement results. Importantly, our protocol works without two-qubit gates, so our protocol is suitable for the devices designed for QA. We also provide numerical calculations to show that our protocol leads to a more accurate estimation of the ground energy than the conventional QA under decoherence.