A general method to construct mean field counter diabatic driving for quantum annealing

Quantum annealing (QA) has been attracted much attention as a method for searching a ground state of quantum many-body systems. Generally, QA requires sufficiently slow dynamics to satisfy adiabatic conditions. The counter-diabatic (CD) driving is known to suppress non-adiabatic transitions and enables fast quantum annealing. However, constructing the CD term requires obtaining the exact eigenstates through classical computation in advance, and due to the non-local nature of the CD term, experimental implementation poses challenges.

In this study, we propose a general and practical method to obtain the Mean field (MF) approximated CD term by using the MF dynamics of magnetization. In our approach, there is no need to solve the self-consistent equations at each time step, and only the initial configuration needs to be provided. We numerically demonstrate that the dynamics with the MF approximated CD term reproduces the self-consistent solution. Using this method, we perform QA for quantum spin glass and demonstrate that the ground state with high fidelity can be obtained compared to the conventional QA. Furthermore, we experimentally demonstrate our method by using a D-wave quantum annealer, Advantage, and obtain the experimental result supporting our numerical simulation. This paper was based on results obtained from a project, JPNP16007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO), Japan.