Pattern-Dependent Performance of the Bernstein-Vazirani Algorithm

Quantum Physics arXiv:2511.14821 (quant-ph) [Submitted on 18 Nov 2025] Title:Pattern-Dependent Performance of the Bernstein-Vazirani Algorithm Authors:Muhammad AbuGhanem View a PDF of the paper titled Pattern-Dependent Performance of the Bernstein-Vazirani Algorithm, by Muhammad AbuGhanem View PDF HTML (experimental) Abstract:Quantum computers promise to redefine the boundaries of computational science, offering the potential for exponential speedups in solving complex problems across chemistry, optimization, and materials science. Yet, their practical utility remains constrained by unpredictable performance degradation under real-world noise conditions. A key question is how problem structure itself influences algorithmic resilience. In this work, we present a comprehensive, hardware-aware benchmarking study of the Bernstein-Vazirani algorithm across 11 diverse test patterns on multiple superconducting quantum processors, revealing that algorithmic performance is exquisitely sensitive to problem structure. Our results reveal average success rates of 100.0\% (ideal simulation), 85.2\% (noisy emulation), and 26.4\% (real hardware), representing a dramatic 58.8\% average performance gap between noisy emulation and real hardware execution. With quantum state tomography confirming corresponding average state fidelities of 0.993, 0.760, and a 0.234 fidelity drop to hardware. Performance degrades dramatically from 75.7\% success for sparse patterns to complete failure for high-density 10-qubit patterns. Most strikingly, quantum state tomography reveals a near-perfect correlation between pattern density and state fidelity degradation, providing the fundamental explanation for observed performance patterns. The catastrophic fidelity collapse observed in real hardware measurements -- dropping to 0.111 compared to the predicted 0.763 -- underscores severe limitations in current noise models for capturing structure-dependent error mechanisms. Our work establishes pattern-dependent performance as a critical consideration for quantum algorithm deployment and provides a quantitative framework for predicting algorithm feasibility in practical applications. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.14821 [quant-ph] (or arXiv:2511.14821v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.14821 Focus to learn more arXiv-issued DOI via DataCite Submission history From: M AbuGhanem [view email] [v1] Tue, 18 Nov 2025 15:36:14 UTC (16,575 KB) Full-text links: Access Paper: View a PDF of the paper titled Pattern-Dependent Performance of the Bernstein-Vazirani Algorithm, by Muhammad AbuGhanemView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?)