Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment

Quantum Physics [Submitted on 16 Apr 2026] Tensor Networks with Belief Propagation Cannot Feasibly Simulate Google's Quantum Echoes Experiment Pablo Bermejo, Benjamin Villalonga, Brayden Ware, Guifre Vidal, Aaron Szasz 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: 37 pages, 28 figures 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 Submission history From: Aaron Szasz [view email] [v1] Thu, 16 Apr 2026 18:00:01 UTC (8,536 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)