Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915254975332352 |
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| author | Lisart-Liebermann, Théo Medina, Arcesio Castañeda |
| author_facet | Lisart-Liebermann, Théo Medina, Arcesio Castañeda |
| contents | The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection of classical optimizer becomes a critical factor in assessing and exploiting quantum-classical applications. One promising approach to tackle these challenges involves incorporating curvature information into the parameter update. The most prominent methods in this field are quasi-Newton and quantum natural gradient methods, which can facilitate faster convergence compared to first-order approaches. Second order methods however exhibit a significant trade-off between computational cost and accuracy, as well as heightened sensitivity to noise. This study evaluates the performance of three families of optimizers on synthetically generated MaxCut problems on a shallow QAOA algorithm. To address noise sensitivity and iteration cost, we demonstrate that incorporating secant-penalization in the BFGS update rule (SP-BFGS) yields improved outcomes for QAOA optimization problems, introducing a novel approach to stabilizing BFGS updates against gradient noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark Lisart-Liebermann, Théo Medina, Arcesio Castañeda Computational Engineering, Finance, and Science Quantum Physics The optimization of parametric quantum circuits is technically hindered by three major obstacles: the non-convex nature of the objective function, noisy gradient evaluations, and the presence of barren plateaus. As a result, the selection of classical optimizer becomes a critical factor in assessing and exploiting quantum-classical applications. One promising approach to tackle these challenges involves incorporating curvature information into the parameter update. The most prominent methods in this field are quasi-Newton and quantum natural gradient methods, which can facilitate faster convergence compared to first-order approaches. Second order methods however exhibit a significant trade-off between computational cost and accuracy, as well as heightened sensitivity to noise. This study evaluates the performance of three families of optimizers on synthetically generated MaxCut problems on a shallow QAOA algorithm. To address noise sensitivity and iteration cost, we demonstrate that incorporating secant-penalization in the BFGS update rule (SP-BFGS) yields improved outcomes for QAOA optimization problems, introducing a novel approach to stabilizing BFGS updates against gradient noise. |
| title | Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark |
| topic | Computational Engineering, Finance, and Science Quantum Physics |
| url | https://arxiv.org/abs/2504.16518 |