Soft-Quantum Algorithms

Quantum Physics [Submitted on 7 Apr 2026] Soft-Quantum Algorithms Basil Kyriacou, Mo Kordzanganeh, Maniraman Periyasamy, Alexey Melnikov Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters via gradient descent. The high cost of training and low fidelity of current quantum devices, however, restricts much of quantum machine learning to classical simulation. For few-qubit problems with large datasets, training the matrix elements directly, as is done with weight matrices in classical neural networks, can be faster than decomposing data and parameters into gates. We propose a method that trains matrices directly while maintaining unitarity through a single regularization term added to the loss function. A second training step, circuit alignment, then recovers a gate-based architecture from the resulting soft-unitary. On a five-qubit supervised classification task with 1000 datapoints, this two-step process produces a trained variational circuit in under four minutes, compared to over two hours for direct circuit training, while achieving lower binary cross-entropy loss. In a second experiment, soft-unitaries are embedded in a hybrid quantum-classical network for a reinforcement learning cartpole task, where the hybrid agent outperforms a purely classical baseline of comparable size. Comments: 6 pages, 6 figures, 0 tables Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI); Machine Learning (cs.LG) Cite as: arXiv:2604.06523 [quant-ph]   (or arXiv:2604.06523v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.06523 Focus to learn more Submission history From: Alexey Melnikov [view email] [v1] Tue, 7 Apr 2026 23:30:40 UTC (240 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.AI cs.LG 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?)