For years, the quantum computing community has benchmarked its progress using simplified, independent noise models, leaving us to navigate the complexities of large-scale devices largely by feel. This commentary analyzes Google's recent out-of-time-order correlator (OTOC) experiments on the 65-qubit Willow processor (Nature 646, 825–830, 2025) and proposes that the primary value of the technique is as a new diagnostic tool rather than a pure quantum-advantage benchmark. The method, combining OTOC measurements with a Pauli insertion protocol, provides a direct, quantitative probe of many-body quantum interference. Two quantitative findings anchor the argument: (1) a simple independent-error model undershoots the observed SNR by roughly an order of magnitude (χ²/ν ≈ 14.2; experimental SNR 3.9 vs. model 0.4), and (2) the Pauli-insertion protocol differentiates small-loop and large-loop interference, with 1-ρ ≈ 0.003 for OTOC⁽¹⁾ versus 1-ρ ≈ 0.445 for OTOC⁽²⁾. We score these results against Gil Kalai's 2016 and 2023 predictions about correlated noise, finding direct experimental signatures for most of his claims. This follow-up to the author's 2024 analysis of Google Willow reframes a quantum-advantage result as the first scalable stethoscope for correlated noise in large quantum processors.
For years, the quantum computing community has benchmarked its progress using simplified, independent noise models, leaving us to navigate the complexities of large-scale devices largely by feel. This commentary analyzes Google's recent out-of-time-order correlator (OTOC) experiments on the 65-qubit Willow processor (Nature 646, 825–830, 2025) and proposes that the primary value of the technique is as a new diagnostic tool rather than a pure quantum-advantage benchmark. The method, combining OTOC measurements with a Pauli insertion protocol, provides a direct, quantitative probe of many-body quantum interference. Two quantitative findings anchor the argument: (1) a simple independent-error model undershoots the observed SNR by roughly an order of magnitude (χ²/ν ≈ 14.2; experimental SNR 3.9 vs. model 0.4), and (2) the Pauli-insertion protocol differentiates small-loop and large-loop interference, with 1-ρ ≈ 0.003 for OTOC⁽¹⁾ versus 1-ρ ≈ 0.445 for OTOC⁽²⁾. We score these results against Gil Kalai's 2016 and 2023 predictions about correlated noise, finding direct experimental signatures for most of his claims. This follow-up to the author's 2024 analysis of Google Willow reframes a quantum-advantage result as the first scalable stethoscope for correlated noise in large quantum processors.
For years, the quantum computing community has benchmarked its progress using simplified, independent noise models, leaving us to navigate the complexities of large-scale devices largely by feel. This commentary analyzes Google's recent out-of-time-order correlator (OTOC) experiments on the 65-qubit Willow processor (Nature 646, 825–830, 2025) and proposes that the primary value of the technique is as a new diagnostic tool rather than a pure quantum-advantage benchmark. The method, combining OTOC measurements with a Pauli insertion protocol, provides a direct, quantitative probe of many-body quantum interference. Two quantitative findings anchor the argument: (1) a simple independent-error model undershoots the observed SNR by roughly an order of magnitude (χ²/ν ≈ 14.2; experimental SNR 3.9 vs. model 0.4), and (2) the Pauli-insertion protocol differentiates small-loop and large-loop interference, with 1-ρ ≈ 0.003 for OTOC⁽¹⁾ versus 1-ρ ≈ 0.445 for OTOC⁽²⁾. We score these results against Gil Kalai's 2016 and 2023 predictions about correlated noise, finding direct experimental signatures for most of his claims. This follow-up to the author's 2024 analysis of Google Willow reframes a quantum-advantage result as the first scalable stethoscope for correlated noise in large quantum processors. --- Zenodo Record --- Version: 2.0 Publication date: 2026-04-19 --- Creators --- - --- Related Identifiers --- - URL: https://doi.org/10.13140/RG.2.2.30911.01443 - DOI: 10.1038/s41586-025-09526-6 - DOI: 10.13140/RG.2.2.28780.63363
The dynamics of quantum many-body systems is characterized by quantum observables that are reconstructed from correlation functions at separate points in space and time1–3. In dynamics with fast entanglement generation, however, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. To circumvent this limitation and enable access to relevant dynamics in experimental systems, repeated time-reversal protocols have been successfully implemented4. Here we experimentally measure the second-order out-of-time-order correlators (OTOC(2))5–18 on a superconducting quantum processor and find that they remain sensitive to the underlying dynamics at long timescales. Furthermore, OTOC(2) manifests quantum correlations in a highly entangled quantum many-body system that are inaccessible without time-reversal techniques. This is demonstrated through an experimental protocol that randomizes the phases of Pauli strings in the Heisenberg picture by inserting Pauli operators during quantum evolution. The measured values of OTOC(2) are substantially changed by the protocol, thereby revealing constructive interference between Pauli strings that form large loops in the configuration space. The observed interference mechanism also endows OTOC(2) with high degrees of classical simulation complexity. These results, combined with the capability of OTOC(2) in unravelling useful details of quantum dynamics, as shown through an example of Hamiltonian learning, indicate a viable path to practical quantum advantage. Experimental measurements of high-order out-of-time-order correlators on a superconducting quantum processor show that these correlators remain highly sensitive to the quantum many-body dynamics in quantum computers at long timescales.
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.
Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC(2). In contrast to dynamics without time reversal, OTOC(2) are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC(2) values. This indicates that OTOC(2) is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC(2) with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC(2) measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC(2), our results indicate a viable path to practical quantum advantage.
Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each OTOC(k) measures the 2k-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.
Abstract We present a purely theoretical proposal, independent of any industrial collaboration, to probe out-of-time-ordered correlators OTOC (2) via information-gauge Wilson loops . Within the renormalizable unified entanglement–entropy quantum field theory (IG–RUEQFT), we treat the information current J μ info as a dynamical variable minimally coupled to an information–gauge field A μ . Our loop-based interpretation yields falsifiable predictions for holonomy responses (perimeter/area mixtures and harmonic content) near the edge of ergodicity , and specifies measurement protocols that can be instantiated on diverse quantum platforms. Building on recent OTOC(2) interferometry on superconducting processors, we design hardware-ready protocols for Google’s platform that (i) map holonomies via phase-programmable insertions, (ii) isolate large-loop (off-diagonal) interference through diagonal/off-diagonal separation, and (iii) quantify information-current fronts and flux from spatiotemporal OTOC(2) gradients. The framework yields falsifiable predictions, including loop-size scaling laws near the edge of ergodicity, phase (holonomy) response maps with harmonic structure from path ordering, and crossed-loop commutator signals diagnosing non-commutative curvature. We specify an analysis pipeline with SNR targets, bootstrap uncertainty estimates, and model selection against classical nulls (Clifford surrogates, cached Monte Carlo, tensor-network contraction), together with robustness checks to disentangle noise from genuine loop phases. The resulting experiments target a practically accessible regime in which echo-enhanced OTOC(2) retains gauge phases long enough to differentiate IG–RUEQFT loop physics from alternative explanations, enabling a concrete, platform-level test of information-gauge curvature and its role in late-time quantum interference.