A general method to construct mean field counter diabatic driving for a ground state search

TL;DR

This paper introduces a mean field-based method to construct local counter diabatic driving terms for quantum annealing, enabling efficient ground state search in complex models like spin glasses, with both numerical and experimental validation.

Contribution

The authors develop a general mean field approach to approximate counter diabatic driving with local operators, making it feasible for experimental quantum annealing.

Findings

MFCD driving achieves high-fidelity ground state search.

Numerical results show MF dynamics with MFCD matches self-consistent MF theory.

Experimental results on a D-wave quantum annealer support the method.

Abstract

The counter diabatic (CD) driving has attracted much attention for suppressing non-adiabatic transition in quantum annealing (QA). However, it can be intractable to construct the CD driving in the actual experimental setup due to the non-locality of the CD dariving Hamiltonian and necessity of exact diagonalization of the QA Hamiltonian in advance. In this paper, using the mean field (MF) theory, we propose a general method to construct an approximated CD driving term consisting of local operators. We can efficiently construct the MF approximated CD (MFCD) term by solving the MF dynamics of magnetization using a classical computer. As an example, we numerically perform QA with MFCD driving for the spin glass model with transverse magnetic fields. We numerically show that the MF dynamics with MFCD driving is equivalent to the solution of the self-consistent equation in MF theory. Also, we clarify that a ground state of the spin glass model with transverse magnetic field can be obtained with high fidelity compared to the conventional QA without the CD driving. Moreover, we experimentally demonstrate our method by using a D-wave quantum annealer and obtain the experimental result supporting our numerical simulation.