Benchmarking Lie-Algebraic Pretraining and Non-Variational QWOA for the MaxCut Problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912791886036992 |
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| author | Zering, Matthaus Joyce, Jolyon Gurfinkel, Tal Wang, Jingbo |
| author_facet | Zering, Matthaus Joyce, Jolyon Gurfinkel, Tal Wang, Jingbo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22856 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Benchmarking Lie-Algebraic Pretraining and Non-Variational QWOA for the MaxCut Problem Zering, Matthaus Joyce, Jolyon Gurfinkel, Tal Wang, Jingbo Quantum Physics 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. |
| title | Benchmarking Lie-Algebraic Pretraining and Non-Variational QWOA for the MaxCut Problem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.22856 |