Random layers for quantum optimal control with exponential expressivity
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Quantum Physics arXiv:2603.08948 (quant-ph) [Submitted on 9 Mar 2026] Title:Random layers for quantum optimal control with exponential expressivity Authors:Marco Dall'Ara, Martin Koppenhöfer, Florentin Reiter, Thomas Wellens, Simone Montangero, Walter Hahn View a PDF of the paper titled Random layers for quantum optimal control with exponential expressivity, by Marco Dall'Ara and 5 other authors View PDF HTML (experimental) Abstract:A long-standing challenge in quantum optimal control is finding an optimal pulse structure that leads to an efficient exploration of the unitary space with a minimal number of optimization parameters. We solve this challenge by constructing parametrized pulse sequences from random constant-amplitude pulses grouped in layers with one optimization parameter per layer. We show that, when increasing the number of pulses, the resulting random unitaries converge exponentially fast to the uniform Haar-random ensemble. Grouping the pulses into layers allows to lower the total number of optimization parameters. We focus on two random-layer (RALLY) methods: In RALLY$_\text{T}$, time durations of the layers are optimized while the pulse amplitudes are randomly chosen beforehand, possibly even from a few discrete values. RALLY$_\text{A}$ optimizes a joint scaling factor of the random pulse amplitudes in each layer. We numerically validate the two methods by applying them to problems of unitary synthesis, ground-state preparation and state transfer in different quantum systems. For all problems considered, both methods approach an information-theoretic lower bound on the number of optimization parameters and outperform other commonly used algorithms. In gradient-free optimization, the RALLY methods are orders of magnitude more accurate with fewer figure-of-merit evaluations. The RALLY methods are also applicable for enhanced quantum machine learning and variational quantum algorithms. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.08948 [quant-ph] (or arXiv:2603.08948v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.08948 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Walter Hahn [view email] [v1] Mon, 9 Mar 2026 21:29:33 UTC (1,109 KB) Full-text links: Access Paper: View a PDF of the paper titled Random layers for quantum optimal control with exponential expressivity, by Marco Dall'Ara and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)