Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment
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Quantum Physics arXiv:2604.15427 (quant-ph) [Submitted on 16 Apr 2026] Title:Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment Authors:Pablo Bermejo, Benjamin Villalonga, Brayden Ware, Guifre Vidal, Aaron Szasz View a PDF of the paper titled Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment, by Pablo Bermejo and 4 other authors View PDF HTML (experimental) Abstract:In the recent quantum echoes experiment, Google Quantum AI showed that out-of-time-order correlators (OTOCs) for random-circuit time evolution can be measured using a quantum processor more than 10,000x faster than they can be computed to similar accuracy via classical computation. This claim was substantiated by comparison with a variety of state-of-the-art classical simulation methods. One classical simulation method that was not explicitly tested was tensor networks with belief propagation (TNBP). TNBP should be poorly suited to simulating Google's echoes experiment: the states involved are highly entangled, a challenge for tensor network states; and the Willow chip has dense 2D connectivity, a challenge for belief propagation. Here we confirm, via a combination of theoretical scaling arguments and explicit numerical simulation, the intuition that TNBP is unable to simulate the quantum echoes experiment. We show that the OTOC circuits generate enough entanglement that they are largely incompressible, implying that other approaches in which OTOCs are computed by evolving a tensor network state in the Schrödinger picture will also fail. Our results further reinforce the claim that the quantum echoes experiment cannot be reproduced by classical computation. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.15427 [quant-ph] (or arXiv:2604.15427v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.15427 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Aaron Szasz [view email] [v1] Thu, 16 Apr 2026 18:00:01 UTC (8,536 KB) Full-text links: Access Paper: View a PDF of the paper titled Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment, by Pablo Bermejo and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 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?)