The Cost of Certainty: Shot Budgets in Quantum Program Testing

Quantum Physics arXiv:2510.22418 (quant-ph) [Submitted on 25 Oct 2025] Title:The Cost of Certainty: Shot Budgets in Quantum Program Testing Authors:Andriy Miranskyy View a PDF of the paper titled The Cost of Certainty: Shot Budgets in Quantum Program Testing, by Andriy Miranskyy View PDF HTML (experimental) Abstract:As quantum computing advances toward early fault-tolerant machines, testing and verification of quantum programs become urgent but costly, since each execution consumes scarce hardware resources. Unlike in classical software testing, every measurement must be carefully budgeted. This paper develops a unified framework for reasoning about how many measurements are required to verify quantum programs. The goal is to connect theoretical error bounds with concrete test strategies and to extend the analysis from individual tests to full program-level verification. We analyze the relationship between error probability, fidelity, trace distance, and the quantum Chernoff bound to establish fundamental shot count limits. These foundations are applied to three representative testing methods: the inverse test, the swap test, and the chi-square test. Both idealized and noisy devices are considered. We also introduce a program-level budgeting approach that allocates verification effort across multiple subroutines. The inverse test is the most measurement efficient, the swap test requires about twice as many shots, and the chi-square test is easiest to implement but often needs orders of magnitude more measurements. In the presence of noise, calibrated baselines may increase measurement requirements beyond theoretical estimates. At the program level, distributing a global fidelity target across many fine-grained functions can cause verification costs to grow rapidly, whereas coarser decompositions or weighted allocations remain more practical. The framework clarifies trade-offs among different testing strategies, noise handling, and program decomposition. It provides practical guidance for budgeting measurement shots in quantum program testing, helping practitioners balance rigour against cost when designing verification strategies. Subjects: Quantum Physics (quant-ph); Software Engineering (cs.SE) Cite as: arXiv:2510.22418 [quant-ph] (or arXiv:2510.22418v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.22418 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Andriy Miranskyy [view email] [v1] Sat, 25 Oct 2025 19:34:16 UTC (110 KB) Full-text links: Access Paper: View a PDF of the paper titled The Cost of Certainty: Shot Budgets in Quantum Program Testing, by Andriy MiranskyyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cs cs.SE 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?)