Statistical Benchmarking of Six Optimization Methods for Variational Quantum Eigensolver under Noise Conditions

Quantum Physics arXiv:2510.08727 (quant-ph) [Submitted on 9 Oct 2025] Title:Statistical Benchmarking of Optimization Methods for Variational Quantum Eigensolver under Quantum Noise Authors:Silvie Illésová, Tomáš Bezděk, Vojtěch Novák, Bruno Senjean, Martin Beseda View a PDF of the paper titled Statistical Benchmarking of Optimization Methods for Variational Quantum Eigensolver under Quantum Noise, by Silvie Ill\'esov\'a and Tom\'a\v{s} Bezd\v{e}k and Vojt\v{e}ch Nov\'ak and Bruno Senjean and Martin Beseda View PDF HTML (experimental) Abstract:This work investigates the performance of numerical optimization algorithms applied to the State-Averaged Orbital-Optimized Variational Quantum Eigensolver for the H2 molecule under various quantum noise conditions. The goal is to assess the stability, accuracy, and computational efficiency of commonly used gradient-based, gradient-free, and global optimization strategies within the Noisy Intermediate-Scale Quantum regime. We systematically compare six representative optimizers, BFGS, SLSQP, Nelder-Mead, Powell, COBYLA, and iSOMA,under ideal, stochastic, and decoherence noise models, including phase damping, depolarizing, and thermal relaxation channels. Each optimizer was tested over multiple noise intensities and measurement settings to characterize convergence behavior and sensitivity to noise-induced landscape distortions. The results show that BFGS consistently achieves the most accurate energies with minimal evaluations, maintaining robustness even under moderate decoherence. COBYLA performs well for low-cost approximations, while SLSQP exhibits instability in noisy regimes. Global approaches such as iSOMA show potential but are computationally expensive. These findings provide practical guidance for selecting suitable optimizers in variational quantum simulations, highlighting the importance of noise-aware optimization strategies for reliable and efficient quantum chemistry computations on current hardware. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.08727 [quant-ph] (or arXiv:2510.08727v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.08727 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Silvie Illésová [view email] [v1] Thu, 9 Oct 2025 18:34:11 UTC (751 KB) Full-text links: Access Paper: View a PDF of the paper titled Statistical Benchmarking of Optimization Methods for Variational Quantum Eigensolver under Quantum Noise, by Silvie Ill\'esov\'a and Tom\'a\v{s} Bezd\v{e}k and Vojt\v{e}ch Nov\'ak and Bruno Senjean and Martin BesedaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)