Benchmarking Lie-Algebraic Pretraining and Non-Variational QWOA for the MaxCut Problem

TL;DR

This paper compares Lie-algebraic pretraining and non-variational QWOA strategies for improving the trainability of quantum algorithms on MaxCut problems, showing that NV-QWOA achieves high approximation ratios with fewer parameters.

Contribution

It introduces and benchmarks two novel strategies—Lie algebraic pretraining and non-variational QWOA—for enhancing quantum algorithm trainability on MaxCut, demonstrating their effectiveness over standard methods.

Findings

NV-QWOA achieves 98.9% approximation ratio in 60 iterations.

Lie-algebraic pretrained QWOA reaches 77.71% after 500 iterations.

Both methods outperform standard random initialization QAOA.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a leading candidate for achieving quantum advantage in combinatorial optimization on Near-Term Intermediate-Scale Quantum (NISQ) devices. However, random initialization of the variational parameters typically leads to vanishing gradients, rendering standard variational optimization ineffective. This paper provides a comparative performance analysis of two distinct strategies designed to improve trainability: Lie algebraic pretraining framework that uses Lie-algebraic classical simulation to find near-optimal initializations, and non-variational QWOA (NV-QWOA) that targets a restrict parameter subspace covered by 3 hyperparameters. We benchmark both methods on the unweighted Maxcut problem using a circuit depth of $p = 256$ across 200 Erd\H{o}s-R\'enyi and 200 3-regular graphs, each with 16 vertices. Both approaches significantly improve upon the standard randomly initialized QWOA. NV-QWOA attains a mean approximation ratio of 98.9\% in just 60 iterations, while the Lie-algebraic pretrained QWOA improves to 77.71\% after 500 iterations. That optimization proceeds more quickly for NV-QWOA is not surprising given its significantly smaller parameter space, however, that an algorithm with so few tunable parameters reliably finds near-optimal solutions is remarkable. These findings suggest that the structured parameterization of NV-QWOA offers a more robust training approach than pretraining on lower-dimensional auxiliary problems. Future work is needed to confirm scaling to larger problem sizes and to asses generalization to other problem classes.