AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking

Quantum Physics [Submitted on 2 Apr 2026] AQ-Stacker: An Adaptive Quantum Matrix Multiplication Algorithm with Scaling via Parallel Hadamard Stacking Wladimir Silva 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: 10 pages, 3 figures 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 Submission history From: Wladimir Silva [view email] [v1] Thu, 2 Apr 2026 21:29:57 UTC (1,115 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)