Reliable Optimization Under Noise in Quantum Variational Algorithms
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911259526430720 |
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| author | Novák, Vojtěch Illésová, Silvie Bezděk, Tomáš Zelinka, Ivan Beseda, Martin |
| author_facet | Novák, Vojtěch Illésová, Silvie Bezděk, Tomáš Zelinka, Ivan Beseda, Martin |
| contents | The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We investigate this phenomenon by benchmarking eight classical optimizers spanning gradient-based, gradient-free, and metaheuristic methods on quantum chemistry Hamiltonians H$_2$, H$_4$ chain, LiH (in both full and active spaces) using the truncated Variational Hamiltonian Ansatz. We analyze difficulties of gradient-based methods (e.g., SLSQP, BFGS) in noisy regimes, where they diverge or stagnate. We show that the bias of estimator can be corrected by tracking the \textit{population mean}, rather than the biased best individual when using population based optimizer. Our findings, which are shown to generalize to hardware-efficient circuits and condensed matter models, identify adaptive metaheuristics (specifically CMA-ES and iL-SHADE) as the most effective and resilient strategies. We conclude by presenting a set of practical guidelines for reliable VQE optimization under noise, centering on the co-design of physically motivated ansatz and the use of adaptive optimizers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_08289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reliable Optimization Under Noise in Quantum Variational Algorithms Novák, Vojtěch Illésová, Silvie Bezděk, Tomáš Zelinka, Ivan Beseda, Martin Quantum Physics 81P68, 90C30, 65K10, 68Q12, 62L20 F.2.1; F.1.2; G.1.6; I.2.8 The optimization of Variational Quantum Eigensolver is severely challenged by finite-shot sampling noise, which distorts the cost landscape, creates false variational minima, and induces statistical bias called winner's curse. We investigate this phenomenon by benchmarking eight classical optimizers spanning gradient-based, gradient-free, and metaheuristic methods on quantum chemistry Hamiltonians H$_2$, H$_4$ chain, LiH (in both full and active spaces) using the truncated Variational Hamiltonian Ansatz. We analyze difficulties of gradient-based methods (e.g., SLSQP, BFGS) in noisy regimes, where they diverge or stagnate. We show that the bias of estimator can be corrected by tracking the \textit{population mean}, rather than the biased best individual when using population based optimizer. Our findings, which are shown to generalize to hardware-efficient circuits and condensed matter models, identify adaptive metaheuristics (specifically CMA-ES and iL-SHADE) as the most effective and resilient strategies. We conclude by presenting a set of practical guidelines for reliable VQE optimization under noise, centering on the co-design of physically motivated ansatz and the use of adaptive optimizers. |
| title | Reliable Optimization Under Noise in Quantum Variational Algorithms |
| topic | Quantum Physics 81P68, 90C30, 65K10, 68Q12, 62L20 F.2.1; F.1.2; G.1.6; I.2.8 |
| url | https://arxiv.org/abs/2511.08289 |