Lyapunov Controlled Counterdiabatic Quantum Optimization

TL;DR

This paper presents a novel quantum algorithm that combines counterdiabatic protocols with Lyapunov control to improve combinatorial optimization, reducing complexity and enhancing adaptability for near-term quantum devices.

Contribution

It introduces a versatile quantum optimization method integrating CD protocols with QLC, reducing reliance on complex higher-order terms and classical optimization.

Findings

Enhanced solution quality over traditional CD methods

Reduced dependence on higher-order CD terms

Applicable to near-term quantum hardware

Abstract

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.