Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark

• URL: http://arxiv.org/abs/2504.16518v1
• Date: Wed, 23 Apr 2025 08:44:18 GMT
• Title: Preconditioning Natural and Second Order Gradient Descent in Quantum Optimization: A Performance Benchmark
• Authors: Théo Lisart-Liebermann, Arcesio Castañeda Medina,
• Abstract summary: We introduce a novel approach to stabilizing BFGS updates against gradient noise.<n>To address noise sensitivity we show that incorporating apenalization in the BFGS update improved outcomes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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