Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice

[2408.03073] Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2408.03073 (quant-ph) [Submitted on 6 Aug 2024] Title: Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice Authors: Tim Schwägerl , Yahui Chai , Tobias Hartung , Karl Jansen , Stefan Kühn View a PDF of the paper titled Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice, by Tim Schw\"agerl and 4 other authors View PDF HTML (experimental) Abstract: Variational quantum algorithms and, in particular, variants of the varational quantum eigensolver have been proposed to address combinatorial optimization (CO) problems. Using only shallow ansatz circuits, these approaches are deemed suitable for current noisy intermediate-scale quantum hardware. However, the resources required for training shallow variational quantum circuits often scale superpolynomially in problem size. In this study we numerically investigate what this scaling result means in practice for solving CO problems using Max-Cut as a benchmark. For fixed resources, we compare the average performance of training a shallow variational quantum circuit, sampling with replacement, and a greedy algorithm starting from the same initial point as the quantum algorithm. We identify a minimum problem size for which the quantum algorithm can consistently outperform sampling and, for each problem size, characterize the separation between the quantum algorithm and the greedy algorithm. Furthermore, we extend the average case analysis by investigating the correlation between the performance of the algorithms by instance. Our results provide a step towards meaningful benchmarks of variational quantum algorithms for CO problems for a realistic set of resources. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2408.03073 [quant-ph] (or arXiv:2408.03073v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2408.03073 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Quantum Mach. Intell. 8, 26 (2026) Related DOI : https://doi.org/10.1007/s42484-026-00355-y Focus to learn more DOI(s) linking to related resources Submission history From: Tim Schwägerl [ view email ] [v1] Tue, 6 Aug 2024 09:57:34 UTC (457 KB) Full-text links: Access Paper: View a PDF of the paper titled Benchmarking Variational Quantum Algorithms for Combinatorial Optimization in Practice, by Tim Schw\"agerl and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2024-08 References & Citations INSPIRE HEP NASA ADS Google 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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