{"id":"ef2c7450-4aec-4016-ba4b-ac15440f04db","arxiv_id":"2412.17454","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A sensitivity-adaptive closed-loop optimizer with signal pre-distortion achieves 0.09(10)% controlled-Z gate error (about 99.9% fidelity) in 64 ns on fixed-frequency superconducting qubits.","lead":"Researchers optimized the shape of control pulses for a two-qubit gate on superconducting chips and reached 99.9% fidelity in 64 nanoseconds. The method adapts its own error sensitivity during calibration and corrects distortions in the control wiring, which could speed up tune-up of quantum processors.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unmeasured coupler leakage is the load-bearing weak point: the 0.09(10)% IRB error for the 64 ns Fourier,C pulse can be biased toward higher fidelity because leaked coupler population is invisible to qubit-only readout, so the 'above 99.9%' claim is not yet established.","rationale":"I agree with the Pith reader that unmeasured coupler leakage is the most load-bearing assumption. The paper itself flags this limitation, and the final Fourier,C pulse is the one used for the abstract and Section V claim, so the missing verification directly touches the central result. The quoted uncertainty (0.09(10)%) is too large to claim 99.9% on statistical grounds alone, but the leakage channel is the more serious issue because it can produce a systematic overestimate of fidelity rather than a mere loss of precision. The concrete test above is feasible: the authors already have a cryoscope-based method to sense the coupler through Q1, and a leakage-detection sequence would settle whether the 0.09% IRB number is real. The rest of the paper is careful and the optimization and distortion-mitigation methodology are credible, so I would keep the reader's CONDITIONAL verdict rather than reject outright. The verdict should remain CONDITIONAL: accept the method, but require a leakage-sensitive fidelity measurement (or an explicit leakage bound) before the 99.9% headline is asserted.","tokens_in":20727,"tokens_out":12973,"duration_ms":125913,"concrete_test":"Run a leakage-robust IRB variant on the same 64 ns Fourier,C pulse: before the qubit readout of each randomized sequence, apply a calibrated mapping pulse that transfers any coupler excitation to Q1 (for example, a fast passage across the |1,00> to |0,01> avoided crossing, using the same coupler-sensing technique already demonstrated in the cryoscope extension of Appendix D), then read out Q1 and Q2. Compare the extracted interleaved gate error to the reported 0.09(10)%. If the leakage-aware error is significantly larger (for instance above 0.2%), the IRB fidelity was inflated by unmeasured coupler leakage and the 'above 99.9%' claim is not supported; if the result reproduces 0.09(10)% within statistical error, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline result (Section V, 'average gate fidelities above 99.9%') rests on the interleaved randomized benchmarking (IRB) estimate epsilon_Fourier,C = 0.09(10)% for the 64 ns Fourier-series pulse. IRB measures only the two qubit states; population that leaks into the tunable coupler is not registered. The authors state in Section IV that 'the coupler states are not directly measurable on the current device' and that numerical simulations identify coupler states as the main leakage channel. They also report leakage signatures for the Fourier-series pulse in IRB, with the PiCoS pulse presented as reducing leakage. If a fraction of the order of 0.1-0.2% remains in the coupler at readout, the qubit readout sees |0>, which is exactly the success outcome of an RB sequence, so the leaked population is counted as fidelity rather than error. Since the claimed fidelity margin is only 0.09(10)% against the 99.9% threshold, this unmeasured channel is not a negligible correction: it is the difference between supporting and not supporting the central claim. No leakage-robust RB analysis, coupler-state post-selection, or equivalent verification is provided for the final Fourier,C pulse.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports closed-loop, sensitivity-adaptive CMA-ES optimization of controlled-Z gates on fixed-frequency transmons coupled through a tunable coupler. Three pulse parametrizations (Gaussian-square, Fourier-series, and PiCoS) are compared using ORBIT/RB-derived costs, and the authors identify flux-line distortions with an extended cryoscope protocol, apply IIR/FIR pre-distortion, and report a final interleaved randomized benchmarking error of 0.09(10)% for a 64 ns Fourier-series pulse, summarized as \"average gate fidelities above 99.9%\". The appendices provide device parameters, leakage and ZZ-phase characterization, optimization details and runtime analysis, and a description of the distortion-correction filter model.","tokens_in":21058,"tokens_out":5333,"duration_ms":50175,"significance":"If the headline error is unbiased, this is a useful practical demonstration: a 64 ns CZ gate with roughly 0.1% error on fixed-frequency transmons with a tunable coupler, obtained by combining black-box closed-loop optimization with independent line-distortion characterization. The strengths of the paper are the explicit sensitivity-adaptive cost schedule, the systematic comparison across parametrizations, and the cryoscope-based IIR/FIR correction with an independently measured step response. The main caveat is that the fidelity metric is qubit-only interleaved randomized benchmarking, with an unmeasured coupler-leakage channel, so the \"above 99.9%\" claim is not yet fully established.","major_comments":[{"comment":"The headline claim rests on interleaved randomized benchmarking, which records only qubit states. The manuscript explicitly states that the coupler states are not directly measurable on the current device and that numerical simulations identify coupler states as the dominant leakage channel, and the earlier Fourier-series pulse already shows leakage signatures in IRB. For the final Fourier,C pulse, only \"minimal indications of leakage\" are reported, without a quantitative bound or a leakage-robust analysis. Since leaked coupler population that returns to |0> at readout is counted as a successful RB outcome, an unquantified leakage of order 0.1% would directly move the reported 0.09(10)% error across the 99.9% boundary. Please provide either a leakage-robust RB estimate, a numerical master-equation bound on coupler population during the 64 ns pulse, or an explicitly weakened claim that does not assert fidelity above 99.9%.","section":"Section IV, final paragraph; Fig. 4(c)"},{"comment":"The statement \"average gate fidelities above 99.9%\" is not supported by the reported IRB error epsilon_Fourier,C = 0.09(10)%. With the stated uncertainty, the interval extends to about 0.19% error (99.81% fidelity) or beyond, so the data do not demonstrate that the fidelity is above 99.9%. Please report the uncertainty model used for the IRB estimates and either soften the claim to \"about 99.9%\" or provide a confidence-level statement for exceeding the 99.9% threshold.","section":"Section V, first and last paragraphs; Section IV, Fig. 4(c)"}],"minor_comments":[{"comment":"The row labels in Table II appear transposed relative to the text: the row with np=8 and 0.52(15)% should be the Fourier-series pulse, the row with np=21 and 0.25(9)% should be the PiCoS pulse, the row with np=8 and 0.09(10)% should be Fourier,C, and the row with np=21 and 0.21(9)% should be PiCoS,C.","section":"Table II"},{"comment":"The parameter count for the Fourier-series decomposition is inconsistent: Section III states eight parameters, Section IV says \"five Fourier-components\", and Table II (as printed) lists np=21 for the Fourier row; please state the count consistently in all three places.","section":"Section III and Section IV"},{"comment":"The caption contains the duplicated phrase \"as shown is shown in Fig. 3(c)\", and the shading change used to indicate sensitivity updates is not explained in the caption.","section":"Fig. 3 caption"},{"comment":"The sentence reporting the PiCoS 20 ns pulse with a 12 ns buffer would benefit from explicitly stating whether the 0.21(9)% error refers to the total gate duration or only the active pulse width, since the table lists tp=20 ns and tb=12 ns separately.","section":"Section IV, paragraph on PiCoS pulse"}],"recommendation":"major_revision","confidential_remarks":"This is a technically solid experimental methods paper. The main gating factor is the unmeasured coupler-leakage channel; given the authors' own statement that coupler states are not directly measurable, the headline should be softened unless a leakage-robust RB analysis or a credible numerical leakage bound is added. I do not see grounds for rejection, but the revision needs to address the statistical basis of the 99.9% claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing to know: this is a solid experimental calibration paper, not a physics breakthrough. The genuinely useful contribution is showing that closed-loop CMA-ES optimization combined with a cryoscope-extracted flux pre-distortion can push a 64 ns CZ gate to ~0.1% error on a fixed-frequency/tunable-coupler architecture. That is an engineering data point worth having. What the paper does well: the sensitivity-adaptive schedule (increase Clifford count when cost drops below 0.2) is a simple, sensible tweak to ORBIT; the extension of cryoscope to measure the coupler response through the qubit is practical; and the systematic identification of long-time-scale flux distortions as the residual error source is the most valuable part. The authors are also honest that coupler states are not measurable and that leakage into them remains unverified.\n\nThe soft spots are real but mostly addressable. The headline 'average gate fidelities above 99.9%' is not strictly supported by their own number: ϵ = 0.09(10)% has a 95% interval that includes 0.19%, i.e. 99.81%. So the claim should be 'around 99.9%' or 'up to 99.9%'. More importantly, the leakage caveat is load-bearing. The authors state that numerical simulations identify coupler states as the main leakage channel, and that the Fourier pulse shows leakage signatures in IRB. Since coupler population returning to |0> looks like success in a qubit-only readout, an IRB estimate that misses that channel can be biased optimistic. For the final 64 ns Fourier pulse, no leakage-robust RB or coupler-state verification is provided. I don't think this is fatal—they are transparent about it, and the PiCoS pulse is explicitly presented as mitigating leakage—but it means the 99.9% claim is not established.\n\nMinor but annoying: Table II has the PiCoS and Fourier rows swapped relative to the text (np, pulse duration, and error values are interchanged). The parameter count also drifts: abstract says seven parameters, Section III says eight, Table II lists 8 and 21. That suggests a hasty final edit.\n\nBottom line: the method works and the paper deserves peer review. A referee should ask for a softened fidelity claim or a leakage measurement, and for the table/count fixes. If you work on tune-up or calibration of superconducting processors, this is worth citing; it is not going to change the physics landscape.","headline":"A solid experimental calibration study with a real engineering payoff, but the 99.9% fidelity headline overreaches its own error bar and the unmeasured coupler leakage keeps that claim from being established.","tokens_in":21654,"tokens_out":3941,"would_cite":true,"duration_ms":34798,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.67.Lx","85.25.-j"],"model":"deepseek-v4-flash","headline":"A sensitivity-adaptive closed-loop optimizer, combined with signal pre-distortion, pushes controlled-Z gate error to 0.09(10)% in a 64 ns pulse on fixed-frequency superconducting qubits, reaching average gate fidelities above 99.9%.","keywords":["superconducting qubits","controlled-Z gate","tunable coupler","closed-loop optimization","randomized benchmarking","pulse shaping","flux-line distortion correction","CMA-ES"],"falsifier":"Measure the coupler-state population after the optimized 64 ns Fourier pulse: a device whose tunable coupler is coupled to its own readout resonator could reveal, in a Ramsey or population-measurement sequence, whether a non-negligible fraction of the population sits in the $|1,01\\rangle$ or $|2,00\\rangle$ states at the end of the pulse. If a substantial fraction is found and does not coherently return to the qubit subspace, the reported 0.09(10)% underestimates the true gate error; if the coupler is found empty, the interleaved-randomized-benchmarking number is a faithful measure of gate fidelity. A leakage-sensitive variant of randomized benchmarking that tracks these states would serve the same purpose without new hardware.","tokens_in":20523,"feed_emoji":"⚛️","tokens_out":24054,"duration_ms":191513,"temperature":0.7,"pith_summary":"Long, fast two-qubit gates are the usual fidelity bottleneck in superconducting quantum processors, and this paper claims a practical route past it: a closed-loop optimizer that tunes the coupler-flux pulse directly on the device, using a randomized-benchmarking cost function whose sensitivity is continuously adapted as the candidates improve. On a pair of fixed-frequency superconducting qubits (transmons) coupled through a flux-tunable coupler, the method calibrates a 64 ns Fourier-series controlled-Z pulse — the standard entangling gate that gives the $|11\\rangle$ state an extra $\\pi$ phase — defined by only a handful of parameters, to a gate error of 0.09(10)%, an average fidelity above 99.9%. The second ingredient is systematic correction of the flux line: inspecting the shapes the optimizer converged to revealed microsecond-scale low-pass distortions, and compensating them with on-device pre-distortion dropped the error of the same pulse family from about 0.6% to 0.09%. Three pulse parametrizations (Gaussian-square, Fourier-series, and piecewise-constant-slope) are compared, and the pipeline is offered as a general tune-up and recalibration method for superconducting processors.","feed_headline":"Closed-loop tuning hits 99.9% two-qubit fidelity in 64 ns","feed_subtitle":"Adaptive pulse optimization plus pre-distortion pushes controlled-Z error below 0.1% on superconducting qubits.","key_machinery":"The central object is the flux pulse together with the feedback loop that shapes it. The gate itself is produced by the conditional frequency shift $\\xi$, tuned by threading external flux $\\Phi_{\\mathrm{ext}}$ through the coupler's SQUID loop so that the $|11\\rangle$ state accumulates a $\\pi$ phase; how fast the pulse traverses the avoided crossing at $\\Phi^{\\star}$ decides how much population leaks to the $|1,01\\rangle$ and $|2,00\\rangle$ states and whether Landau-Zener-Stückelberg interference returns it. The feedback loop is a CMA-ES optimizer (covariance-matrix-adaptation evolution strategy) minimizing an ORBIT cost function built from randomized-benchmarking sequences, with the sensitivity $S = dE/d\\epsilon$ kept near its maximum by increasing the number of Clifford gates $N$ whenever the mean cost drops below 0.2. Pulse shapes are parametrized as Gaussian-square, Fourier-series, or piecewise-constant-slope (PiCoS) forms; the Fourier envelope is $\\Phi(t) = A \\sum_{n=1}^{N} \\lambda_n \\left(1 - \\cos\\left(2\\pi n (t - t_p/2)/\\tau_w\\right)\\right)$ with few coefficients. The last ingredient is distortion correction: an extended cryoscope protocol (a pulse-based measurement of the flux-line step response) measures the coupler's response through the fixed-frequency qubit, and four exponential IIR filters plus a 72-tap FIR filter running in real time on the arbitrary waveform generator compress the flux-line response time from 2.5 µs to 10 ns.","core_discovery":"The paper's central claim is that closed-loop optimization with an adaptive cost function, combined with signal pre-distortion, reaches average controlled-Z gate fidelities above 99.9%: reoptimized 64 ns Fourier-series pulses achieve $\\epsilon_{\\mathrm{Fourier,C}} = 0.09(10)\\%$ gate error. The gate is implemented by adiabatically sweeping a tunable coupler's frequency so that the conditional frequency shift $\\xi$ — the extra phase accumulated by the $|11\\rangle$ state relative to the other computational states — integrates to $\\pi$, while Landau-Zener-Stückelberg interference recovers population that leaks through avoided crossings during the outbound and return passages. The paper compares three pulse parametrizations: a Gaussian-square pulse reaching about 4.79% error; a Fourier-series pulse at 0.62(15)% error before correction and 0.09(10)% after pre-distortion; and a piecewise-constant-slope (PiCoS) pulse at 0.25(9)% before correction and 0.21(9)% at a shorter 20 ns pulse plus a 12 ns buffer after correction. The authors interpret the converged pulse shapes as encoding the hardware's systematic errors, in particular low-pass filtering of the flux line with time constants up to 2.5 µs, and show that correcting this transfer function in real time on the waveform generator is what unlocks the sub-0.1% regime. The same closed-loop scheme is proposed for tune-up and recalibration of superconducting quantum processors.","pith_inferences":["The headline number's own uncertainty is large: at 0.09(10)%, the measured error is within one standard deviation of zero, so the claim of 'above 99.9%' would be sharpened by a longer interleaved randomized benchmarking run or by an independent fidelity estimate that does not rely on the same leakage-blind decay model.","Because the paper's stated limitation is that coupler states cannot be read out, a decisive follow-up is to run the identical optimization on a device where the coupler has its own dispersive readout; if population is found to linger in the coupler after the 64 ns pulse, both the 0.09% number and the leakage-free interpretation of the converged pulse would need revision.","The converged pulse shapes are described as encoding the flux-line transfer function, so one could formalize the pipeline to output, in a single run, both the optimal pulse and an empirical distortion model usable for open-loop design on future chips — turning what is here a two-step procedure (optimize, then characterize) into a single self-characterizing calibration."],"forward_implications":["If the 0.09(10)% error holds, the CZ gate ceases to be the fidelity bottleneck on this architecture: a 64 ns two-qubit gate at 99.9% average fidelity on fixed-frequency transmons with a tunable coupler is practical, and the same closed-loop recipe can be applied to every qubit pair on a chip.","The adaptive sensitivity rule removes the need to preset the benchmarking depth: the optimizer starts at short sequences suitable for poor candidates and lengthens them as candidates improve, so one run carries the gate from roughly 50% error to the 0.1% regime without manual retuning.","Recalibration after parameter drift can reuse the converged covariance matrices, and the identified distortion model shortens later optimizations (from 12 h to 4.5 h in the demonstrated case), supporting the paper's proposal of interleaving optimization with algorithmic tasks to track drift in real time.","The parametrization comparison indicates that control complexity and hardware correction are partly interchangeable: before pre-distortion the 21-parameter PiCoS pulse beats the simpler Fourier pulse, while after pre-distortion the simpler Fourier pulse reaches the lowest error, suggesting that adding correction hardware can buy simpler pulses."],"supporting_citations":[{"why":"This reference establishes the adiabatic conditional-phase gate scheme via tunable ZZ interactions and the adiabaticity limit that fixes the pulse-speed constraint.","marker":"[21]"},{"why":"This reference supplies the fixed-frequency-transmon plus tunable-coupler architecture with a zero-ZZ idle point that the experiment realizes.","marker":"[23]"},{"why":"This reference provides the asymmetric floating-coupler design whose two coupling paths cancel the idle ZZ shift.","marker":"[27]"},{"why":"This reference supplies the closed-loop optimal-control approach with a randomized-benchmarking cost function and leakage reduction that the paper's method extends.","marker":"[35]"},{"why":"This reference provides the Landau-Zener-Stückelberg interference model used to explain how leakage across the avoided crossings is recovered.","marker":"[41]"},{"why":"This reference gives the ORBIT randomized-benchmarking cost function that serves as the optimization objective.","marker":"[44]"},{"why":"This reference supplies the CMA-ES evolution strategy used to search the pulse parameters and handle correlations between them.","marker":"[46]"},{"why":"This reference provides the interleaved randomized benchmarking protocol that produces the reported gate-error numbers.","marker":"[49]"},{"why":"This reference supplies the cryoscope protocol that the paper extends to measure flux-line distortions through a fixed-frequency qubit.","marker":"[54]"},{"why":"This reference documents the arbitrary waveform generator hardware whose real-time IIR and FIR filters implement the pre-distortion.","marker":"[55]"}],"fun_headline_variants":["Adaptive closed-loop tuning reaches 99.9% CZ gate fidelity in 64 ns","Sub-0.1% two-qubit error via sensitivity-adaptive pulse shaping","Signal pre-distortion unlocks 99.9% fidelity in 64 ns CZ gates","Closed-loop optimization with adaptive sensitivity hits 0.09% gate error","Sensitivity-adaptive loops plus pre-distortion beat 0.1% CZ error"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central number assumes that interleaved randomized benchmarking reports the true gate error even though the experiment never directly checks for population leaking into the coupler: if population leaves the two qubits during the 64 ns pulse and returns only during the measurement, the reported error could be smaller than the actual gate error, a limitation the paper states explicitly in Section IV.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive closed-loop tuning reaches 99.9% CZ gate fidelity in 64 ns","Sub-0.1% two-qubit error via sensitivity-adaptive pulse shaping","Signal pre-distortion unlocks 99.9% fidelity in 64 ns CZ gates","Closed-loop optimization with adaptive sensitivity hits 0.09% gate error","Sensitivity-adaptive loops plus pre-distortion beat 0.1% CZ error"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000906,"raw_usage":{"total_tokens":3966,"prompt_tokens":1085,"completion_tokens":2881,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":701,"completion_tokens_details":{"reasoning_tokens":2770}},"tokens_in":701,"tokens_out":2881,"duration_ms":21186,"temperature":1.0,"reasoning_tokens":2770,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T05:26:53.923536+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the coupler-state population after the optimized 64 ns Fourier pulse: a device whose tunable coupler is coupled to its own readout resonator could reveal, in a Ramsey or population-measurement sequence, whether a non-negligible fraction of the population sits in the $|1,01\\rangle$ or $|2,00\\rangle$ states at the end of the pulse. If a substantial fraction is found and does not coherently return to the qubit subspace, the reported 0.09(10)% underestimates the true gate error; if the coupler is found empty, the interleaved-randomized-benchmarking number is a faithful measure of gate fidelity. A leakage-sensitive variant of randomized benchmarking that tracks these states would serve the same purpose without new hardware.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference establishes the adiabatic conditional-phase gate scheme via tunable ZZ interactions and the adiabaticity limit that fixes the pulse-speed constraint."},{"cited_title":"Stehlik, D","cited_arxiv_id":null,"evidence_quote":"This reference supplies the fixed-frequency-transmon plus tunable-coupler architecture with a zero-ZZ idle point that the experiment realizes."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference provides the asymmetric floating-coupler design whose two coupling paths cancel the idle ZZ shift."},{"cited_title":"Werninghaus, D","cited_arxiv_id":null,"evidence_quote":"This reference supplies the closed-loop optimal-control approach with a randomized-benchmarking cost function and leakage reduction that the paper's method extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference provides the Landau-Zener-Stückelberg interference model used to explain how leakage across the avoided crossings is recovered."},{"cited_title":"Kelly, R","cited_arxiv_id":null,"evidence_quote":"This reference gives the ORBIT randomized-benchmarking cost function that serves as the optimization objective."},{"cited_title":"Magesan, J","cited_arxiv_id":null,"evidence_quote":"This reference provides the interleaved randomized benchmarking protocol that produces the reported gate-error numbers."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"This reference documents the arbitrary waveform generator hardware whose real-time IIR and FIR filters implement the pre-distortion."}],"review_version":1}