Mean Field Quantum Annealing Correction

Abstract

In this review, how quantum annealing correction works is described from the statistical physics point of view. Quantum annealing correction (QAC) is a programmable error correction scheme in quantum annealing. It is designed to suppress errors by imposing energy penalties. There have been various experimental tests on D-wave machines demonstrating that QAC significantly improves the success probabilities of finding ground states of Ising models. We analyze QAC in the ferromagnetic and Hopfield models by using the mean field theory. The results of our analyses show that QAC efficiently suppresses the thermal fluctuations. In addition, it can significantly increase the energy gap during annealing by changing the energy penalties. In some instances, exponentially small energy gaps turn into polynomially small energy gaps. This suggests that QAC can drastically improve the computational efficiency.