A Square-Root Barrier to Quantum Gate Speed under Linear Coupling

Quantum Physics arXiv:2609.19280 (quant-ph) [Submitted on 16 Sep 2026] Title:A Square-Root Barrier to Quantum Gate Speed under Linear Coupling Authors:Pablo Restrepo Gaviria, Mischa P. Woods View a PDF of the paper titled A Square-Root Barrier to Quantum Gate Speed under Linear Coupling, by Pablo Restrepo Gaviria and Mischa P. Woods View PDF HTML (experimental) Abstract:Faster quantum gates can suppress the decoherence accumulated during a computation, but in superconducting processors stronger microwave pulses can also increase leakage, off-resonant excitation, stray-field errors, and crosstalk. This creates a central energy--speed--error tradeoff: can quantum state engineering make a gate parametrically faster without paying proportionally more drive energy? We address this question by treating the driving pulse as a quantum bosonic field rather than a classical waveform. For a finite-dimensional system coupled linearly to that field, we prove that fixed-fidelity gate transition rates grow at most as the square root of the pulse energy, under stated uniformity conditions on the coupling and accepted dynamics. The bound permits arbitrary pulse states, including squeezed and non-Gaussian states, as well as drive--system entanglement and back action; coherent Gaussian pulses attain its energy exponent. Thus squeezing or other state engineering alone cannot replace the square-root energy law of a conventional linear drive by the linear scaling allowed by general quantum speed limits. Achieving that improvement requires changing the interaction class, in addition to using a suitable nonclassical pulse, thereby identifying interaction nonlinearity as an essential resource for relaxing the practical gate-speed error tradeoff. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2609.19280 [quant-ph] (or arXiv:2609.19280v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.19280 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mischa Woods Dr [view email] [v1] Wed, 16 Sep 2026 18:00:11 UTC (486 KB) Full-text links: Access Paper: View a PDF of the paper titled A Square-Root Barrier to Quantum Gate Speed under Linear Coupling, by Pablo Restrepo Gaviria and Mischa P. WoodsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: math math-ph math.MP physics physics.comp-ph 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?)