Iterative Matrix Product State Simulation for Scalable Grover's Algorithm
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Quantum Physics arXiv:2601.03832 (quant-ph) [Submitted on 7 Jan 2026] Title:Iterative Matrix Product State Simulation for Scalable Grover's Algorithm Authors:Mei Ian Sam, Tzu-Ling Kuo, Tai-Yue Li View a PDF of the paper titled Iterative Matrix Product State Simulation for Scalable Grover's Algorithm, by Mei Ian Sam and 2 other authors View PDF HTML (experimental) Abstract:Grover's algorithm is a cornerstone of quantum search algorithm, offering quadratic speedup for unstructured problems. However, limited qubit counts and noise in today's noisy intermediate-scale quantum (NISQ) devices hinder large-scale hardware validation, making efficient classical simulation essential for algorithm development and hardware assessment. We present an iterative Grover simulation framework based on matrix product states (MPS) to efficiently simulate large-scale Grover's algorithm. Within the NVIDIA CUDA-Q environment, we compare iterative and common (non-iterative) Grover's circuits across statevector and MPS backends. On the MPS backend at 29 qubits, the iterative Grover's circuit runs about 15x faster than the common (non-iterative) Grover's circuit, and about 3-4x faster than the statevector backend. In sampling experiments, Grover's circuits demonstrate strong low-shot stability: as the qubit number increases beyond 13, a single-shot measurement still closely mirrors the results from 4,096 shots, indicating reliable estimates with minimal sampling and significant potential to cut measurement costs. Overall, an iterative MPS design delivers speed and scalability for Grover's circuit simulation, enabling practical large-scale implementations. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.03832 [quant-ph] (or arXiv:2601.03832v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.03832 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Tai-Yue Li [view email] [v1] Wed, 7 Jan 2026 11:55:26 UTC (1,459 KB) Full-text links: Access Paper: View a PDF of the paper titled Iterative Matrix Product State Simulation for Scalable Grover's Algorithm, by Mei Ian Sam and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)