{"id":"261abb25-bd19-4fba-a294-0a3b4ca91e13","arxiv_id":"2411.10206","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A teleportation-based protocol with Riemannian Trust-Region circuit compilation estimates the butterfly velocity of the XY model on a noisy simulator, matching the analytical maximum group velocity.","lead":"This paper demonstrates a way to measure the butterfly velocity, the speed at which quantum information spreads, in a 1D spin chain by running a quantum teleportation protocol on a noisy quantum simulator. The authors combine two existing techniques and find their estimates agree with the exact analytical speed to within a few percent.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The relation between measured F_EPR and OTOC is internally contradictory: Eq. (15) gives F_EPR = ⟨OTOC⟩/4, while Section IV uses C = 2 − 1/(2F_EPR), which requires ⟨OTOC⟩ = 1/(4F_EPR). The reported butterfly velocities rest on an unsupported mapping.","rationale":"In good faith, the paper's analytical fermionization in Section II and Appendix A is standard and internally consistent, and the Table I values are close to the analytical maximum group velocity, which gives some independent support. The central claim, however, is the proof-of-concept demonstration that the YKY-RTR protocol measures the butterfly velocity on NISQ devices. That claim depends on converting the measured teleportation probability F_EPR into the squared commutator C_j(t). The paper gives two incompatible relations for this conversion: Eq. (15) and the Section IV formula. The reader's weakest assumption focused on the arbitrary threshold and finite-size effects; those are legitimate but secondary. The F_EPR relation is load-bearing because if it is wrong, every C_j(t) value, every spreading time, and the resulting velocity in Table I are unfounded. Because the inconsistency may be a fixable typo and the underlying protocol is plausible, the appropriate verdict is conditional rather than rejection: the authors must correct the relation and re-verify the reported numbers. The unresolved '[?]' citations and the use of FakeTorino rather than a real device further support not accepting the demonstration in its current form, but the equation contradiction is the decisive issue.","tokens_in":10860,"tokens_out":10675,"duration_ms":95381,"concrete_test":"For a two-qubit XY chain, analytically compute the exact probability of the '00' outcome on A0/B0 conditioned on the Aj/Bj projection in Figure 2, and compare it with the exact operator-averaged OTOC at the same time. This settles whether F_EPR = (1/4)⟨OTOC⟩ or F_EPR = 1/(4⟨OTOC⟩). Then recompute the spreading times and the Table I velocities from the raw F_EPR data using the correct relation; if the extracted velocities shift by more than the reported few-percent agreement, the central claim fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section III A Eq. (15) states F_EPR = (1/4)⟨OTOC⟩, i.e., ⟨OTOC⟩ = 4F_EPR. The following sentence estimates ⟨OTOC⟩ as 1/(4F_EPR), and Section IV computes C_j(t) = 2 − 1/(2F_EPR), which follows from C = 2 − 2⟨OTOC⟩ only if ⟨OTOC⟩ = 1/(4F_EPR). These two relations are reciprocal and cannot both hold. If Eq. (15) is correct, the C_j(t) values used to extract the butterfly velocities in Table I are wrong; if Section IV is correct, Eq. (15) and the diagrammatic derivation are wrong. Either way the paper does not establish the claimed mapping from the measured teleportation probability to the operator-averaged OTOC, and the proof-of-concept agreement with the maximum group velocity is not supported by the equations as written. This is more fundamental than the reader's threshold/finite-size concern: it concerns the very formula relating the measurement outcome to the OTOC.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper combines the Yoshida-Kitaev-Yao (YKY) teleportation protocol with Riemannian trust-region (RTR) Hamiltonian-to-circuit compilation to estimate the operator-averaged out-of-time-order correlation function and, from it, the butterfly velocity of the one-dimensional XY model. The authors derive the maximum group velocity of the XY model analytically via Jordan-Wigner, Fourier, and Bogoliubov transformations, and then compare these values with velocities extracted from 5-qubit simulations of the YKY-RTR protocol. The numerical results are obtained with the IBM FakeTorino noisy simulator and are reported to agree with the analytical butterfly velocities to within a few percent.","tokens_in":11068,"tokens_out":24554,"duration_ms":226549,"significance":"If the measurement pipeline is correct, the paper offers a useful proof-of-concept for estimating butterfly velocities on near-term devices in models that are not analytically solvable. The analytical derivation in Section II and Appendix A is standard and internally consistent, and the comparison with the independently computed maximum group velocity is a genuine consistency check rather than a fit to the target. The RTR-based circuit compilation is a promising tool for reducing circuit depth relative to product formulas. However, the current manuscript has a load-bearing inconsistency in the relation between the measured teleportation probability and the OTOC, and the numerical extraction lacks the error analysis and hardware context needed to support the claimed few-percent agreement.","major_comments":[{"comment":"Eq. (15) states F_EPR = (1/4)⟨OTOC⟩, while the sentence following it and Section IV use ⟨OTOC⟩ = 1/(4F_EPR), with C_j(t) = 2 - 1/(2F_EPR). These two relations are reciprocal and cannot both hold. A direct two-qubit check (e.g., U = CNOT, for which the operator-averaged OTOC in Eq. (10) equals 1/2 and the conditional Bell probability F_EPR equals 1/2) confirms the reciprocal form used in Section IV, indicating that Eq. (15) and the diagrammatic derivation around Eqs. (16)-(18) contain an inverted factor. Because every numerical C_j(t) value in Section IV is derived from F_EPR, the mapping from the measured probability to the OTOC must be corrected and re-derived before the reported velocities are fully supported; the numerical implementation appears to use the correct form, but the paper as written does not establish the mapping.","section":"Section III A, Eq. (15), and Section IV"},{"comment":"The butterfly-velocity estimates rest entirely on the arbitrary spreading threshold C_j(t) >= 0.1, a linear fit to spreading times t_j over only j = 2, ..., 5 on a 5-qubit chain, and the identification of the fitted slope with the infinite-chain maximum group velocity of Eq. (9). No error bars are reported for the FakeTorino estimates, no sensitivity of t_j or the fitted slope to the threshold is given, and finite-size effects, including the boundary term dropped in Eq. (4), are not assessed. These omissions are load-bearing because the claimed few-percent agreement in Table I could be coincidental for a single threshold choice.","section":"Section IV, Table I, Fig. 4"},{"comment":"The abstract claims a \"proof-of-concept demonstration of this method to estimate the butterfly velocity on NISQ-devices,\" but all quantum results in Section IV are obtained with the FakeTorino noisy simulator rather than a physical quantum device. This overstates the experimental content of the paper; the claim should be narrowed to a noisy-simulation demonstration or supported by data from actual hardware.","section":"Abstract and Section IV"},{"comment":"The RTR mapping produces a brick-wall circuit of preselected depth m, but the manuscript never states the value of m, the optimization tolerance, the achieved Frobenius error ||E(G) - U||_F, or the number of shots used in the FakeTorino runs. Without these details the numerical results are not reproducible, and the possible bias of the circuit approximation on C_j(t) cannot be assessed.","section":"Sections III B and IV"}],"minor_comments":[{"comment":"The numerator of the group-velocity expression lacks parentheses; as written, it is ambiguous and should be checked against the derivative of Eq. (8).","section":"Eq. (9)"},{"comment":"The unparenthesized expression \"1/4F_EPR\" should be written as \"1/(4F_EPR)\" to avoid ambiguity; this ambiguity is directly related to the inconsistency in Eq. (15).","section":"Section III A"},{"comment":"The text alternates between referring to the final Bell measurement on A1,B1 and on A0,B0; the notation should be made consistent across Eq. (15), the circuit description, and the results section.","section":"Figure 2 and Section IV"},{"comment":"The text contains placeholder citations \"[ ? ]\" for \"standard libraries\" and for the comparison with product formulas; complete references should be supplied.","section":"References [24], [25]"},{"comment":"The column labels \"Numerical 5 qubits\" and \"Quantum 5 qubits\" are not defined in the text; the paper should state whether these are noiseless and FakeTorino results, respectively, and should report the statistical uncertainty of each entry.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely salvageable: the numerical implementation appears to use the correct reciprocal relation between F_EPR and the OTOC, so the inconsistency in Eq. (15) is probably a typographical or derivation error rather than a fundamental flaw. However, the arbitrary threshold, missing error bars, and the simulator-versus-hardware overclaim need to be addressed before the proof-of-concept claim is credible. If the authors can correct the OTOC-F_EPR mapping, add sensitivity analyses, and rephrase the NISQ claim, the manuscript could be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a plausible proof-of-concept, not a breakthrough. The new bit is combining the YKY teleportation protocol with RTR-based Hamiltonian-to-circuit compilation to extract a butterfly velocity from an operator-averaged OTOC, and checking it against the analytic max group velocity of the XY model. The analytic part is standard, but the end-to-end pipeline is a legitimate incremental application.\n\nWhat it does well: the Jordan-Wigner/Fourier/Bogoliubov derivation in Sec II and Appendix A is standard and internally consistent. The numerical values in Table I are within a few percent of the analytic vB, and because the analytic value is computed independently, the comparison is a genuine consistency check, not a fit to the target. Using RTR to build a shallow brick-wall circuit is a reasonable choice, and the paper is honest that the results come from the FakeTorino simulator—but the abstract's 'on NISQ-devices' overstates that, since no real hardware was used.\n\nSoft spots: the threshold C_j >= 0.1 is arbitrary and there are no error bars or sensitivity analysis; the velocity comes from a linear fit over only four lattice positions on a 5-qubit chain, so finite-size/boundary effects could bias the slope. The RTR circuit depth and approximation error are not reported, which matters for assessing whether the compilation step is actually the bottleneck. And there are unresolved '[?]' placeholder citations in Sec III B; the paper is not in submission-ready shape. These are fixable, but they need to be fixed.\n\nOn the stress-test: I don't think the contradiction between Eq. (15) and Sec IV is real. The extracted text's line break obscures the fraction: Eq. (15) is F_EPR = 1/(4⟨OTOC⟩), not (1/4)⟨OTOC⟩. That is exactly the relation used in Sec IV when they compute C_j = 2 - 1/(2F_EPR). So the mapping from teleportation probability to OTOC is internally consistent; the stress-test concern is a formatting artifact.\n\nWho it's for: people building quantum algorithms to measure scrambling or operator growth on near-term devices. It's a small proof-of-concept, not a definitive result. It deserves a serious referee, but with a request for substantial revision: run on real hardware or soften the claim, add error bars/sensitivity analysis, report compilation overhead, and clean up the references.\n\nRecommendation: send it to peer review, conditional on those revisions.","headline":"A plausible proof-of-concept for YKY+RTR butterfly velocity measurement on a simulator, with an overclaimed NISQ framing and some unfinished edges; the alleged OTOC mapping contradiction does not hold up.","tokens_in":11612,"tokens_out":7616,"would_cite":false,"duration_ms":65617,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A teleportation-based OTOC protocol with Riemannian-trust-region circuit compilation estimates the XY model's butterfly velocity on a noisy five-qubit simulation, matching the analytic maximum group velocity.","keywords":["butterfly velocity","out-of-time-order correlator","XY model","quantum teleportation","Riemannian trust-region","operator growth","NISQ devices","Hamiltonian simulation"],"falsifier":"Run the same YKY-RTR measurement on chains of length 7, 9, and 11 qubits, and re-extract the velocity with thresholds $C_j(t)\\ge 0.05$, $0.1$, and $0.2$; if the fitted slope changes systematically with chain length or threshold by more than the few-percent scatter reported here, then the finite-chain linear-fit velocity is not the infinite-chain maximum-group-velocity butterfly velocity.","tokens_in":10631,"feed_emoji":"🦋","tokens_out":12325,"duration_ms":105876,"temperature":0.7,"pith_summary":"The paper establishes a practical path from a quantum many-body Hamiltonian to a measured scrambling speed: it runs a quantum-teleportation protocol that extracts the operator-averaged out-of-time-order correlator (OTOC), a correlation function that tracks how a local operator grows into a many-body operator, and it uses Riemannian trust-region optimization to compile the time-evolution unitary into a short gate circuit. From the OTOC at different lattice sites, the paper defines a spreading time at each site and fits a line whose inverse slope is the butterfly velocity, the speed at which a local perturbation travels through the system. On a noisy simulation of a five-qubit quantum device, the method yields 1.972 for the isotropic XY model and 3.745 for the anisotropic model, against analytic values of 2 and 3.75 obtained from the maximum group velocity. The paper argues that the protocol is robust to certain decoherence and coherent errors without any error-mitigation post-processing, and that the same machinery can be applied to lattice models that are not analytically solvable.","feed_headline":"Five-qubit noisy simulation matches the XY model's butterfly velocity","feed_subtitle":"Teleportation plus Riemannian optimization recovers the analytically predicted scrambling speed in noisy 5-qubit runs.","key_machinery":"Three pieces carry the argument. The YKY teleportation protocol is a doubled-Hilbert-space circuit in which a Bell-basis post-selection probability gives $F_{\\mathrm{EPR}}=1/(4\\langle\\mathrm{OTOC}\\rangle)$, converting operator growth into a measurable teleportation fidelity; the paper uses $F_{\\mathrm{EPR}}$ to compute $C_j(t)=2-1/(2F_{\\mathrm{EPR}})$. The Riemannian trust-region (RTR) optimizer on the product manifold $U(4)^m$ minimizes the Frobenius error $\\|E(G)-e^{-iHt}\\|_F^2$ over $m$-layer brick-wall circuits, producing a compiled unitary that is shallower than product-formula decompositions. The threshold rule $C_j(t)\\ge 0.1$ defines a site-dependent spreading time $t_j$, and the inverse slope of the best-fit line through $t_j$ versus lattice position $j$ is the reported butterfly velocity.","core_discovery":"The central claim is that the butterfly velocity of the one-dimensional anisotropic XY model, defined as the maximum group velocity of its quasiparticles, can be estimated on noisy near-term quantum hardware by combining a teleportation-based OTOC measurement with Riemannian-trust-region (RTR) circuit compilation. Analytically, the paper diagonalizes $H=J\\sum_j(\\frac{1+r}{2}X_jX_{j+1}+\\frac{1-r}{2}Y_jY_{j+1}+hZ_j)$ via Jordan-Wigner, Fourier, and Bogoliubov transformations, obtaining the dispersion $\\varepsilon(k)=-2J\\sqrt{(h-\\cos k)^2+r^2\\sin^2 k}$ and group velocity $v_g(k)=-2J[\\sin k(h-\\cos k)+r^2\\sin k\\cos k]/\\sqrt{(h-\\cos k)^2+r^2\\sin^2 k}$, so $v_B=\\max_k v_g(k)$. Numerically, the YKY teleportation circuit gives the squared commutator $C_j(t)=2-1/(2F_{\\mathrm{EPR}})$ from the teleportation fidelity $F_{\\mathrm{EPR}}$, the spreading time at site $j$ is $t_j=\\min\\{t:C_j(t)\\ge 0.1\\}$, and a least-squares fit to $t_j$ for $j=2,\\ldots,5$ has inverse slope equal to the butterfly velocity. The paper reports that these noisy-simulation estimates agree with the analytic $v_B$ to within a few percent, and that RTR compilation uses significantly fewer circuit layers than Lie-Trotter-Suzuki product formulas.","pith_inferences":["One could turn the fixed threshold into a diagnostic: repeat the $t_j$ extraction at several thresholds and check that the fitted velocity is stable; if it is not, the linear-fit estimator should be replaced by a light-cone-edge extrapolation.","A natural next test would be to apply the same YKY-RTR measurement to a non-integrable or disordered spin chain, where no analytic $v_B$ exists, and compare the output against exact-diagonalization or tensor-network light-cone speeds.","Because the protocol measures $C_j(t)$ separately at each site, it could be adapted to measure asymmetric or directional butterfly velocities, and to extract the full light cone rather than a single speed, in models with anisotropic interactions."],"forward_implications":["On a noisily simulated five-qubit device, the protocol recovers the isotropic XY butterfly velocity within about 1.4 percent (1.972 versus the analytic 2) and the anisotropic value within about 0.1 percent (3.745 versus 3.75).","Because the estimator obeys $1/(4F_{\\mathrm{EPR}}) \\ge \\langle\\mathrm{OTOC}\\rangle$, the protocol inherits a one-sided robustness to decoherence and small coherent errors, so it does not require explicit error mitigation to remain usable near the noise threshold of current devices.","RTR circuit compilation requires substantially fewer layers than Lie-Trotter-Suzuki splitting at the same target error, which is the step that makes the OTOC circuit short enough to run on noisy hardware.","The analytic diagonalization provides a closed-form benchmark, $v_B=\\max_k v_g(k)$, that future hardware measurements on longer chains can be tested against as quantum devices improve."],"supporting_citations":[{"why":"Introduces the teleportation-based protocol whose post-selected Bell measurement is used to estimate the operator-averaged OTOC.","marker":"[19]"},{"why":"Supplies the $F_{\\mathrm{EPR}} = 1/(4\\langle\\mathrm{OTOC}\\rangle)$ relation and the robustness analysis showing that the estimate is insensitive to certain decoherence and coherent errors.","marker":"[20]"},{"why":"Defines the Riemannian trust-region optimization method used to compile the time-evolution unitary into a brick-wall circuit.","marker":"[22]"},{"why":"Provides the manifold-optimization background and convergence properties that justify using RTR on $U(4)^m$.","marker":"[23]"},{"why":"Gives the identification of the butterfly velocity with the maximum quasiparticle group velocity, which the paper's analytic benchmark and numerical comparisons rely on.","marker":"[26]"},{"why":"Yields the $\\mathcal{O}(\\epsilon^{-2})$ sample-complexity bound that supports the claim that a few samples suffice to estimate $F_{\\mathrm{EPR}}$ to additive precision.","marker":"[29]"}],"fun_headline_variants":["Quantum teleportation pins down XY butterfly velocity","Noisy quantum runs match analytic butterfly velocity","Teleportation OTOC measures scrambling speed on NISQ","Riemannian optimization recovers XY scrambling speed","Butterfly velocity from 5-qubit noisy simulation"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the inverse slope of a best-fit line through the spreading times at four lattice sites, fixed by an arbitrary $C_j(t)\\ge 0.1$ threshold on a five-qubit chain, equals the infinite-chain butterfly velocity obtained from the maximum group velocity.","fun_headline_variants_meta":{"raw":{"variants":["Quantum teleportation pins down XY butterfly velocity","Noisy quantum runs match analytic butterfly velocity","Teleportation OTOC measures scrambling speed on NISQ","Riemannian optimization recovers XY scrambling speed","Butterfly velocity from 5-qubit noisy simulation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000212,"raw_usage":{"total_tokens":1443,"prompt_tokens":993,"completion_tokens":450,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":609,"completion_tokens_details":{"reasoning_tokens":375}},"tokens_in":609,"tokens_out":450,"duration_ms":4980,"temperature":1.0,"reasoning_tokens":375,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:50:20.976904+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same YKY-RTR measurement on chains of length 7, 9, and 11 qubits, and re-extract the velocity with thresholds $C_j(t)\\ge 0.05$, $0.1$, and $0.2$; if the fitted slope changes systematically with chain length or threshold by more than the few-percent scatter reported here, then the finite-chain linear-fit velocity is not the infinite-chain maximum-group-velocity butterfly velocity.","supporting_citations":[{"cited_title":"Disentangling scram- bling and decoherence via quantum teleportation","cited_arxiv_id":null,"evidence_quote":"Supplies the $F_{\\mathrm{EPR}} = 1/(4\\langle\\mathrm{OTOC}\\rangle)$ relation and the robustness analysis showing that the estimate is insensitive to certain decoherence and coherent errors."},{"cited_title":"Trust-region methods on riemannian manifolds","cited_arxiv_id":null,"evidence_quote":"Defines the Riemannian trust-region optimization method used to compile the time-evolution unitary into a brick-wall circuit."},{"cited_title":"Lieb-robinson cor- relation function for the quantum transverse-field ising model","cited_arxiv_id":null,"evidence_quote":"Gives the identification of the butterfly velocity with the maximum quasiparticle group velocity, which the paper's analytic benchmark and numerical comparisons rely on."},{"cited_title":"Information scrambling over bipartitions: Equilibration, entropy production, and typicality","cited_arxiv_id":null,"evidence_quote":"Yields the $\\mathcal{O}(\\epsilon^{-2})$ sample-complexity bound that supports the claim that a few samples suffice to estimate $F_{\\mathrm{EPR}}$ to additive precision."}],"review_version":1}