AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking
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Quantum Physics arXiv:2604.02530 (quant-ph) [Submitted on 2 Apr 2026] Title:AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking Authors:Wladimir Silva View a PDF of the paper titled AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking, by Wladimir Silva View PDF HTML (experimental) Abstract:Matrix multiplication (MatMul) is the computational backbone of modern machine learning, yet its classical complexity remains a bottleneck for large-scale data processing. We propose a hybrid quantum-classical algorithm for matrix multiplication based on an adaptive configuration of Hadamard tests. By leveraging Quantum Random Access Memory (QRAM) for state preparation, we demonstrate that the complexity of computing the inner product of two vectors can be reduced to $O(\log N)$. We introduce an "Adaptive Stacking" framework that allows the algorithm to dynamically reconfigure its execution pattern from sequential horizontal stacking to massive vertical parallelism based on available qubit resources. This flexibility enables a tunable time-complexity range, theoretically reaching $O(N^2)$ on fault-tolerant systems while maintaining compatibility with near-term hardware. We validate the numerical stability of our approach through a Quantum Machine Learning (QML) simulation, achieving 96% accuracy on the MNIST handwritten digit dataset. Our results suggest that adaptive quantum MatMul provides a viable path toward super-classical efficiency in high-dimensional linear algebra operations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02530 [quant-ph] (or arXiv:2604.02530v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.02530 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Wladimir Silva [view email] [v1] Thu, 2 Apr 2026 21:29:57 UTC (1,115 KB) Full-text links: Access Paper: View a PDF of the paper titled AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking, by Wladimir SilvaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?) 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?)