Hardware-efficient quantum annealing with error mitigation via classical shadow

Quantum annealing (QA) is an efficient method for finding the ground-state energy of the problem Hamiltonian. However, in practical implementation, the system suffers from decoherence. On the other hand, recently, ``Localized virtual purification" (LVP) was proposed to suppress decoherence in the context of noisy intermediate-scale quantum (NISQ) devices. Suppose observables have spatially local support in the lattice. In that case, the requirement for LVP is to calculate the expectation value with a reduced density matrix on a portion of the total system. In this work, we propose a method to mitigate decoherence errors in QA using LVP. The key idea is to use the so-called classical shadow method to construct the reduced density matrix. Thanks to the CS, unlike the previous schemes to mitigate decoherence error for QA, we do not need either two-qubit gates or mid-circuit measurements, which means that our method is hardware-efficient.