Entanglement and circuit complexity in finite-depth random linear optical networks
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Quantum Physics arXiv:2604.14277 (quant-ph) [Submitted on 15 Apr 2026] Title:Entanglement and circuit complexity in finite-depth random linear optical networks Authors:Laura Shou, Joseph T. Iosue, Yu-Xin Wang, Victor Galitski, Alexey V. Gorshkov View a PDF of the paper titled Entanglement and circuit complexity in finite-depth random linear optical networks, by Laura Shou and 4 other authors View PDF HTML (experimental) Abstract:We study the growth of entanglement and circuit complexity in random passive linear optical networks as a function of the circuit depth. For entanglement dynamics, we start with an initial Gaussian state with all $n$ modes squeezed. For random brickwall circuits, we show that entanglement, as measured by the Rényi-2 entropy, grows at most diffusively as a function of the depth. In the other direction, for arbitrary circuit geometries we prove bounds on depths which ensure the average subsystem entanglement reaches within a constant factor of the maximum value in all subsystems, and bounds which ensure closeness of the random linear optical unitary to a Haar random unitary in $L^2$ Wasserstein distance. We also consider robust circuit complexity for random one-dimensional brickwall circuits, as measured by the minimum number of gates required in any circuit that approximately implements the linear optical unitary. Viewing this as a function of the number of modes and the circuit depth, we show the robust circuit complexity for random one-dimensional brickwall circuits scales at most diffusively in the depth with high probability. The corresponding Gaussian unitary $\tilde{\mathcal U}$ for the approximate implementation retains high output fidelity $|\langle\psi|\mathcal U^\dagger \tilde{\mathcal U}|\psi\rangle|^2$ for pure states $|\psi\rangle$ with constrained expected photon-number. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR) Cite as: arXiv:2604.14277 [quant-ph] (or arXiv:2604.14277v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.14277 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Laura Shou [view email] [v1] Wed, 15 Apr 2026 18:00:00 UTC (645 KB) Full-text links: Access Paper: View a PDF of the paper titled Entanglement and circuit complexity in finite-depth random linear optical networks, by Laura Shou and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: math math-ph math.MP math.PR 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?)