  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.
