Structure-Agnostic Unitary Learning from Quantum Observable Dynamics with Application to Hamiltonian Identification

Quantum Physics arXiv:2607.15316 (quant-ph) [Submitted on 16 Jul 2026] Title:Structure-Agnostic Unitary Learning from Quantum Observable Dynamics with Application to Hamiltonian Identification Authors:Mohamed Berkani View a PDF of the paper titled Structure-Agnostic Unitary Learning from Quantum Observable Dynamics with Application to Hamiltonian Identification, by Mohamed Berkani View PDF HTML (experimental) Abstract:We present a variational algorithm for learning an unknown quantum unitary from time-series observable measurements, with no structural assumption about the target. The core separation: a hardware-efficient parametrised circuit learns the evolution operator U via observable matching; Hamiltonian identification follows as classical post-processing via matrix logarithm, when the target happens to be exp(-iH*tau). Three experiments establish the method's generality. First, a noiseless proof of correctness with exact gradients (L-BFGS-B) achieves MSE 1.61e-14 and recovers all Hamiltonian coefficients to six decimal places. Second, a gate-learning experiment fits CNOT, iSWAP, and a Haar-random SU(4) element -- none generated by any fixed Hamiltonian -- all to process fidelity 1.000000, confirming the method does not rely on Trotterisation structure. Third, quantum deployment via SPSA-Adam under Qiskit Aer depolarising noise (p1=0.001, p2=0.01, Nshots=1024) recovers all three Ising Hamiltonian terms with errors below 8%. The optimiser, SPSA-Adam, combines SPSA's hardware-efficient two-point gradient estimation with Adam's adaptive moment updates. A four-stage moment-warm curriculum progressively extends the training horizon, converting a global non-convex problem into a sequence of well-posed local ones. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.15316 [quant-ph] (or arXiv:2607.15316v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.15316 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mohamed Berkani [view email] [v1] Thu, 16 Jul 2026 02:27:54 UTC (15 KB) Full-text links: Access Paper: View a PDF of the paper titled Structure-Agnostic Unitary Learning from Quantum Observable Dynamics with Application to Hamiltonian Identification, by Mohamed BerkaniView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 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?)