Investigating layer-selective transfer learning of QAOA parameters for Max-Cut problem

TL;DR

This paper explores a layer-selective transfer learning approach for QAOA parameters in Max-Cut problems, aiming to reduce optimization complexity and time while maintaining solution quality.

Contribution

It introduces a refinement scheme optimizing only a subset of QAOA layers after parameter transfer, enhancing efficiency for Max-Cut problem solving.

Findings

Selective layer optimization balances solution quality and computational efficiency.

Layer hierarchy impacts the effectiveness of parameter transfer.

The approach scales favorably with problem size.

Abstract

The quantum approximate optimization algorithm (QAOA) is a variational quantum algorithm (VQA) ideal for noisy intermediate-scale quantum (NISQ) processors, and is highly successful in solving combinatorial optimization problems (COPs). It has been observed that the optimal parameters obtained from one instance of a COP can be transferred to another instance, resulting in generally good solutions for the latter. In this work, we propose a refinement scheme in which only a subset of QAOA layers is optimized following parameter transfer, with a focus on the Max-Cut problem. Our motivation is to reduce the complexity of the loss landscape when optimizing all the layers of high-depth QAOA circuits, as well as to reduce the optimization time. We investigate the potential hierarchical roles of different layers and analyze how the approximation ratio scales with increasing problem size. Our findings indicate that the selective layer optimization scheme offers a favorable trade-off between solution quality and computational time, and can be more beneficial than full optimization at a lower optimization time.