Two-parameter counter-diabatic driving in quantum annealing

TL;DR

This paper proposes a two-parameter counter-diabatic approach to quantum annealing in the transverse-field Ising model, enhancing performance and feasibility over existing methods, especially for systems with first-order phase transitions.

Contribution

It introduces a novel two-parameter control scheme that generalizes single-parameter methods, improving convergence and experimental feasibility in quantum annealing.

Findings

Significantly higher ground-state fidelity with the two-parameter method

Lower residual energy compared to traditional and single-parameter approaches

Scaling advantage in time to solution for certain system sizes

Abstract

We introduce a two-parameter approximate counter-diabatic term into the Hamiltonian of the transverse-field Ising model for quantum annealing to accelerate convergence to the solution, generalizing an existing single-parameter approach. The protocol is equivalent to unconventional diabatic control of the longitudinal and transverse fields in the transverse-field Ising model and thus makes it more feasible for experimental realization than an introduction of new terms such as non-stoquastic catalysts toward the same goal of performance enhancement. We test the idea for the $p$-spin model with $p=3$, which has a first-order quantum phase transition, and show that our two-parameter approach leads to significantly larger ground-state fidelity and lower residual energy than those by traditional quantum annealing as well as by the single-parameter method. We also find a scaling advantage in terms of the time to solution as a function of the system size in a certain range of parameters as compared to the traditional methods.