Quantum annealing with error mitigation

TL;DR

This paper introduces a novel error mitigation strategy for quantum annealing that enhances ground-state energy estimation accuracy under decoherence without requiring two-qubit gates.

Contribution

It presents a dual-state purification protocol combining dynamics, measurements, inverse Hamiltonian evolution, and post-processing for noise reduction in QA.

Findings

Improved accuracy of ground energy estimation under decoherence.

Protocol operates without two-qubit gates, suitable for practical devices.

Numerical results demonstrate enhanced performance over conventional QA.

Abstract

Quantum annealing (QA) is one of the efficient methods to calculate the ground-state energy of a problem Hamiltonian. In the absence of noise, QA can accurately estimate the ground-state energy if the adiabatic condition is satisfied. 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. In this paper, 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; the conventional dynamics, single-qubit projective measurements, Hamiltonian dynamics corresponding to an inverse map of the first dynamics, and post-processing of measurement results. Importantly, our protocol works without two-qubit gates, and so our protocol is suitable for the devices designed for practical 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.