Digital-Analog Counterdiabatic Quantum Optimization with Trapped Ions

TL;DR

This paper presents a hybrid digital-analog quantum algorithm tailored for trapped-ion systems to improve optimization problem solving by reducing circuit depth and resource requirements, potentially enabling quantum advantage.

Contribution

It introduces a problem-dependent digital-analog quantum algorithm for optimization, optimizing the use of analog and digital gates in trapped-ion architectures.

Findings

Reduced circuit depth compared to purely digital methods.

Requires fewer resources for maximum independent set problem.

Analog blocks need fidelity below current best to outperform digital simulations.

Abstract

We introduce a hardware-specific, problem-dependent digital-analog quantum algorithm of a counterdiabatic quantum dynamics tailored for optimization problems. Specifically, we focus on trapped-ion architectures, taking advantage from global M{\o}lmer-S{\o}rensen gates as the analog interactions complemented by digital gates, both of which are available in the state-of-the-art technologies. We show an optimal configuration of analog blocks and digital steps leading to a substantial reduction in circuit depth compared to the purely digital approach. This implies that, using the proposed encoding, we can address larger optimization problem instances, requiring more qubits, while preserving the coherence time of current devices. Furthermore, we study the minimum gate fidelity required by the analog blocks to outperform the purely digital simulation, finding that it is below the best fidelity reported in the literature. To validate the performance of the digital-analog encoding, we tackle the maximum independent set problem, showing that it requires fewer resources compared to the digital case. This hybrid co-design approach paves the way towards quantum advantage for efficient solutions of quantum optimization problems.