Classical algorithm inspired by the feedback-based algorithm for quantum optimization and local counterdiabatic driving

TL;DR

This paper introduces CACAO, a classical algorithm inspired by quantum control techniques, which heuristically solves large combinatorial optimization problems by mimicking quantum dynamics.

Contribution

It presents a novel classical algorithm based on quantum Lyapunov control and counterdiabatic driving, bridging quantum and classical optimization methods.

Findings

CACAO performs comparably to quantum algorithms like quantum annealing and FALQON.

The algorithm effectively scales to systems with up to 10,000 spins.

CACAO offers a classical approach inspired by quantum control for large-scale optimization.

Abstract

We propose a quantum-inspired classical algorithm for combinatorial optimization problems, named the counterdiabaticity-assisted classical algorithm for optimization (CACAO). In this algorithm, a solution of a given combinatorial optimization problem is heuristically searched with classical spin dynamics based on quantum Lyapunov control of local counterdiabatic driving. We compare the performance of CACAO with that of quantum time-evolution algorithms, i.e., quantum annealing, the feedback-based algorithm for quantum optimization (known as FALQON), and the counterdiabatic feedback-based quantum algorithm (known as CD-FQA). We also study the performance of CACAO applied to large systems up to $10,000$ spins.