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

• URL: http://arxiv.org/abs/2512.22856v1
• Date: Sun, 28 Dec 2025 09:42:02 GMT
• Title: Benchmarking Lie-Algebraic Pretraining and Non-Variational QWOA for the MaxCut Problem
• Authors: Matthaus Zering, Jolyon Joyce, Tal Gurfinkel, Jingbo Wang,
• Abstract summary: This paper provides a comparative performance analysis of two strategies designed to improve trainability.<n>We benchmark both methods on the unweighted Maxcut problem using a circuit depth of $p = 256$ across 200 Erds-Rényi and 200 3-regular graphs.<n>Both approaches significantly improve upon the standard randomly 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.
• Score: 4.103893081207555
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Erdős-Rényi 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.

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