A new preprint demonstrates that tensor networks paired with belief propagation (TNBP) cannot feasibly simulate Google's quantum echoes experiment, closing a potential loophole in claims of quantum computational advantage. The work, posted to arXiv in April 2026 and not yet peer-reviewed, combines theoretical scaling arguments with explicit numerical simulations on smaller systems (up to roughly 20-30 qubits) to show why classical TNBP methods break down. Researchers extrapolated these results to the full experimental scale involving Google's Willow superconducting processor.

In the original Google experiment, researchers measured out-of-time-order correlators (OTOCs) — quantities that track how quantum information scrambles across a system under random circuit evolution. The quantum hardware performed these calculations more than 10,000 times faster than state-of-the-art classical techniques. While the Google team benchmarked against several classical simulators, they did not explicitly test TNBP, a method that represents quantum states as networks of tensors and uses approximate message-passing (belief propagation) to contract them efficiently.

This preprint confirms the intuition that TNBP is poorly suited here. The random circuits generate high entanglement across a dense 2D qubit lattice, causing the required tensor bond dimensions to explode exponentially. Belief propagation also struggles with the loopy graphical structure of 2D connectivity, leading to uncontrolled approximations. The authors' numerical tests on smaller instances tracked memory and runtime costs, revealing that scaling to the experimental size would demand resources far beyond current supercomputers.

Original coverage of the Google experiment (see Nature Physics papers on related OTOC measurements circa 2022-2024) often emphasized speedup over generic classical simulation but missed explicitly ruling out specialized tensor methods that had narrowed gaps in earlier supremacy experiments like 2019 random circuit sampling. This paper fills that gap. Synthesizing it with the 2019 Google supremacy paper (Nature, arXiv:1910.11333) and a 2023 review on tensor network limitations for 2D quantum systems (Orús et al., arXiv:2301.07526), a clear pattern emerges: while TNBP can approximate some 1D or tree-like systems, highly entangled 2D dynamics create an incompressible representation that defeats these techniques.

What much reporting overlooked is the deeper implication for quantum many-body physics. OTOCs are not just benchmarks — they probe quantum chaos and information scrambling relevant to black hole physics via holography. By showing that even sophisticated classical contraction schemes fail, this work strengthens evidence that the quantum processor is accessing regimes beyond efficient classical description. However, limitations must be noted: the study relies on extrapolation from small numerical simulations rather than full-scale runs, and it focuses solely on Schrödinger-picture evolution, leaving open questions about other potential classical shortcuts.

This result connects to a broader narrative in quantum advantage research. After the 2019 Sycamore claims faced pushback from improved tensor network algorithms, the community has grown more rigorous in benchmarking. The current analysis suggests that for certain 2D entangled dynamics, classical methods face fundamental barriers, not just engineering ones. While not yet peer-reviewed, the combination of analytic bounds and numerical evidence makes a compelling case that Google's quantum echoes experiment stands as persuasive evidence of practical quantum computational advantage.