{"id":"2d0b425f-3778-43a6-9cd6-396866dda53c","arxiv_id":"2507.20100","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"The authors show that a SPICE simulator using classical LCR models can handle 10,000-qubit superconducting readout circuits on a laptop and estimate relative readout fidelity under parameter variations.","lead":"This paper proposes using a standard SPICE circuit simulator to estimate the readout fidelity of superconducting qubit arrays with up to 10,000 qubits, modeling each qubit as a classical LCR circuit. It shows how fabrication-induced variations in capacitors and resistances affect simulated transmission spectra and computed infidelity, aiming for fast early-stage assessment before detailed quantum simulation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. 3's Gamma1 extraction appears to use the resonator peak, whose width is the cavity decay rate kappa, not the qubit T1; the Fig. 5 fidelity values are therefore unvalidated.","rationale":"The reader's CONDITIONAL verdict already names Eq. (3) as the weakest assumption; I agree, but I sharpen the failure mode by pointing to the text's explicit choice of the resonator peaks. In dispersive readout, the resonator-peak linewidth is essentially kappa, so Eq. (3) would extract a cavity photon lifetime rather than qubit T1. The proposed test would settle this by sweeping Rq while holding kappa fixed: a valid qubit-T1 extraction must respond to Rq (plus the Purcell contribution), whereas a kappa measurement will not. If the test confirms the concern, the absolute fidelity values in Fig. 5 are not physically meaningful, although the scalability demonstration and qualitative variability analysis remain useful as an engineering screening tool. If the test refutes it, the method still needs the tau_op calibration the authors acknowledge before it can make quantitative fidelity predictions. The paper's own limitation statements about tau_op and future experimental comparison support a conditional rather than a rejection verdict, so I do not move the reader's overall recommendation.","tokens_in":7172,"tokens_out":11735,"duration_ms":132121,"concrete_test":"Run the single-qubit unit of Fig. 2(b) with the paper's nominal parameters. Vary only the qubit resistance Rq (equivalent to input T1^(q) from 0.5 to 5 microseconds) while holding Cg, Cr, omega_r, and the tank/source loss fixed. For each value, extract delta_omega_p from the resonator peak and from the lower qubit peak, and compare the resulting Gamma1 with the independent dispersive-readout prediction Gamma1 = 1/T1^(q) + g^2*kappa/(Delta^2 + kappa^2/4). If the resonator-peak Gamma1 is insensitive to Rq, Eq. (3) is measuring kappa; if even the qubit-peak Gamma1 fails to match the prediction, the classical linewidth-to-T1 mapping is unjustified.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Eq. (3) is the only bridge from SPICE peak widths to the Gamma1 used in the fidelity formula (Eq. (1)). The paper itself says that, of the two peaks in the AC spectrum, \"Here, we present the resonator peaks\" — the larger peaks at the tank frequencies. For a qubit in the dispersive regime, the resonator-peak width is set by the resonator/environment loss kappa, not by the qubit's energy relaxation rate. Thus T1^(m) = 1/delta_omega_p is the cavity photon lifetime, not the transmon T1. This is compounded by the fact that Rq was already fixed by the input T1^(q) = Cq*Rq, so the simulation cannot independently recover T1; it can only re-emit the input value or, if the wrong peak is used, report kappa. The paper explicitly flags tau_op as experimental and calls for future comparison with experiment, but it does not flag this peak-identification assumption. Unless the selected peak width is shown to track Rq, or to match an independent Purcell-rate calculation, the fidelity distributions in Fig. 5 lack the claimed physical meaning.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a classical SPICE simulation methodology for estimating the readout fidelity of large arrays of transmon qubits. Qubits and resonators are modeled as LCR circuits, the transmission spectrum is computed with LTspice, and the width of the resonator peak is used through Eq. (3) to obtain a relaxation rate Gamma1. This rate, together with an assumed Gamma2 = 2 Gamma1 and a free operation time tau_op, is inserted into the fidelity formula (1) of Abad et al. The authors demonstrate spectra for 4, 100, 1000, and 10,000 qubits under Gaussian parameter variations and compare 'linear' and 'square' layouts, reporting infidelity distributions in Fig. 5. The stated goal is to enable early-stage performance assessment of large-scale superconducting circuits on standard laptops.","tokens_in":7391,"tokens_out":5651,"duration_ms":55752,"significance":"If the physical mapping from the SPICE peak width to the qubit relaxation rate were valid, the scalability claim would be genuinely useful: the reported runtimes (minutes for 1000 qubits, about two hours for 10,000 qubits) are attractive, and the Monte Carlo treatment of fabrication variability is a practical direction for architecture comparison. However, the central fidelity estimate rests on an unvalidated identification of the resonator peak width with the qubit energy relaxation rate, on an assumed Gamma2 = 2 Gamma1 relation, and on a free parameter tau_op that the paper itself says must be determined experimentally. These issues make the absolute infidelity values in Fig. 5 not physically predictive as they stand. The paper's most defensible contribution is the scalable SPICE-based variability analysis; the fidelity interpretation needs substantially more support before the central claim can be accepted.","major_comments":[{"comment":"The paper extracts T1^(m) = 1/delta_omega_p from the resonator peaks in the transmission spectrum. In the dispersive readout regime, the width of the resonator peak is controlled by the cavity photon decay rate kappa and the measurement-line coupling, not by the qubit energy relaxation rate Gamma1. This is not a minor identification issue: Rq has already been fixed by the input relaxation time through Rq = T1^(q)/Cq, so the simulation cannot independently recover the qubit T1; Eq. (3) can only re-express the input value or report kappa. Because Gamma1 in Eq. (1) is taken directly from Eq. (3), the infidelity values in Fig. 5 inherit this unvalidated identification. The authors should validate Eq. (3) against an independent estimate, for example by varying Rq while holding all other parameters fixed and showing that delta_omega_p tracks the expected qubit decay rate, or by comparing with a Purcell-rate calculation.","section":"Eq. (3) and the statement 'Here, we present the resonator peaks'"},{"comment":"The operation time tau_op is introduced as an 'adjustment parameter' that 'should be determined experimentally in the future,' and the paper later states that 'the absolute value of the infidelity should be determined experimentally.' With tau_op free, the vertical scale of Fig. 5 is not a prediction of the simulation; only relative comparisons at fixed tau_op are meaningful. Since the abstract and title promise a method for 'estimating qubit fidelity,' the authors should either compute tau_op from the circuit and readout parameters or explicitly restrict the claim to relative architecture comparison in the abstract and in the Fig. 5 caption.","section":"Fidelity formula (1) and the role of tau_op"},{"comment":"The relation Gamma2 approximately 2 Gamma1 is assumed with no derivation or experimental justification. Since Eq. (1) depends linearly on Gamma1 + Gamma2, any pure-dephasing contribution beyond the T2 = 2T1 limit will change the computed infidelity systematically. The authors should state that this is an ideal-limit assumption and test how the relative comparison between the linear and square architectures changes when Gamma2 is varied over a plausible range.","section":"Assumption Gamma2 approximately 2 Gamma1"},{"comment":"Equation (1) is typeset with a prefactor 'N2N/(2(2N+1))' and the text states that for N=1 the prefactor is 1/3 and that it approaches N/2 for large N. This is internally inconsistent: the N=1 value 1/3 matches a prefactor N/(2N+1), whose large-N limit is 1/2, not N/2. The prefactor controls the N-dependence of the fidelity, so this ambiguity is load-bearing for the 1000- and 10,000-qubit results in Fig. 5. Please correct the expression and re-verify the resulting distributions.","section":"Eq. (1) prefactor and large-N behavior"},{"comment":"The Fig. 5 caption uses tau_op = 10^-11 s for panels (a) and (b) and tau_op = 10^-12 s for panel (c), while the text refers to 'tau_iop' inconsistently. The comparison between the linear and square architectures is therefore ambiguous: if tau_op is the physical measurement time, it should be the same across configurations unless the authors explicitly argue that the readout duration differs, in which case that argument should be made. As written, the conclusion that the linear structure is 'considerably worse' is tied to a chosen free parameter rather than to a fixed operational setting.","section":"Fig. 5 and choice of tau_op"}],"minor_comments":[{"comment":"There are duplicated words and incomplete phrases, for example 'and and the capacitance in qubit Cq' and 'In this study, T1^(q) = Gamma1^-1 = 1 mu.' The latter is missing the time unit (presumably microseconds) and should be completed.","section":"Text around qubit parameters"},{"comment":"The caption refers to 'the linear qubits (Fig. 1(c))', but Fig. 1 is the flowchart; the circuit layout is shown in Fig. 2(c). Please correct the cross-reference.","section":"Fig. 4 caption"},{"comment":"The caption says that in panels (d)-(f) 'out1'-'out4' are the outputs in Fig. 2(e), but Fig. 2(e) is the unit of the square arrangement. The outputs for the linear arrangement are in Fig. 2(c). Please correct the reference.","section":"Fig. 3 caption"},{"comment":"The bibliography contains entries that do not appear to be cited in the text, including 'I. Besedin et al.' and 'A. Miessen et al.' between Refs. 8 and 10. The citation numbering should be checked and repaired throughout.","section":"Reference list"},{"comment":"Equation (4) uses delta_omega in the off-diagonal phase but the connection to the detuning Delta introduced earlier is not stated. Please define delta_omega explicitly.","section":"Eq. (4) notation"}],"recommendation":"major_revision","confidential_remarks":"The central scalability result is plausible and the SPICE simulations appear internally consistent, but the bridge from the classical circuit output to the quantum fidelity numbers is not established. In particular, Eq. (3) identifies the resonator peak width with the qubit energy relaxation rate without validation, and the free parameter tau_op removes the absoluteness of the fidelity claim. This is a fixable but substantive issue: the authors could reframe the paper as a relative architectural-variability comparison, or add a validated mapping from the SPICE observables to Gamma1 and a calibration for tau_op. I would not recommend rejection, but the revision must address the load-bearing mapping before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First thing you should know: the scalability claim survives contact, but the fidelity numbers don't. Running SPICE on 10,000 qubits in a couple of hours on a laptop is a legitimate engineering result, and the Monte Carlo variability study of the transmission spectra gives a useful qualitative picture of how fabrication spreads affect distinguishability. That part is real and worth acknowledging.\n\nThe paper extends the authors' prior SPICE-based T1 estimation to fidelity estimation. The new part is mainly the Monte Carlo treatment of parameter fluctuations and the push to 10,000 qubits; that part is real and worth acknowledging. The runtime figures are plausible for a lumped-element circuit simulation, and the observation that 3% capacitance/inductance spreads blur the peaks of a 200 MHz-spaced array is a useful early-stage screening insight.\n\nHowever, Eq. (3) is a load-bearing problem. T1^(m) = 1/delta_omega_p is taken from the width of the resonator peak—the paper says so explicitly. In dispersive readout that width is the resonator decay rate kappa, not the qubit's energy relaxation rate. The fact that Rq is already set by the input T1^(q) means the simulation cannot independently recover T1; it either re-emits the input or reports the resonator loss, depending on which peak is used. As a result, the infidelity values in Fig. 5 are not physically calibrated. The free parameter tau_op then controls the absolute scale, so agreement with any real device would require tuning two things at once.\n\nThe authors are honest that tau_op needs experiment. But they don't flag the peak-identification issue, and that is the more fundamental one. There are also small mechanical problems: the Cg value is 5 fF in the Fig. 2 caption but 0.1 fF in the text's coupling example; the fidelity formula is garbled in the rendering; and the tau_op values in Fig. 5 differ between panels without discussion.\n\nIf the authors can show that the extracted width tracks the qubit peak (or the Purcell rate), or validate against an independent calculation, the method could become a useful relative screening tool. As it stands, the absolute fidelity claims in the abstract are not supported.\n\nThis is a paper I'd send to a referee, but with the clear instruction that the Gamma1 mapping must be fixed or justified before publication. The qualitative variability analysis deserves to see the light, and the scalability demonstration is of interest to the engineering community.","headline":"Scalability and Monte Carlo variability are real, but the linewidth-to-T1 mapping is a load-bearing flaw that makes the reported fidelities uncalibrated.","tokens_in":7926,"tokens_out":6140,"would_cite":false,"duration_ms":57239,"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 classical SPICE circuit simulator, treating transmon qubits as LCR circuits, estimates readout fidelity for arrays of up to 10,000 qubits on a standard laptop.","keywords":["superconducting qubits","transmon","readout fidelity","SPICE simulation","LCR circuit model","fabrication variability","dispersive readout","Monte Carlo simulation"],"falsifier":"Take a single transmon with a known, independently measured $T_1$, set $R_q = T_1/C_q$ in the SPICE model, extract $\\delta\\omega_p$ from the simulated transmission peak, and compare $1/\\delta\\omega_p$ with the input $T_1$; if the two disagree beyond numerical error, the peak-width mapping is invalid. The same check can be done in hardware by measuring the transmission peak width and the relaxation time of the same device and comparing them.","tokens_in":6950,"feed_emoji":"⚛️","tokens_out":11718,"duration_ms":95373,"temperature":0.7,"pith_summary":"This paper claims that the readout process of transmon superconducting qubits can be simulated by a classical circuit simulator, SPICE (Simulation Program with Integrated Circuit Emphasis), with each qubit and its measurement resonator represented as an LCR circuit. The width of the transmission resonance is converted into a relaxation rate $\\Gamma_1$, which feeds a known fidelity formula, and Monte Carlo trials with Gaussian fabrication variations produce distributions of infidelity. The authors report that 1,000-qubit arrays simulate in minutes and 10,000-qubit arrays in about two hours on a standard laptop. The payoff is a fast, early-stage design screen that compares chip architectures under realistic device variability, before expensive quantum-level simulation or fabrication.","feed_headline":"SPICE estimates 10,000-qubit readout fidelity","feed_subtitle":"Treating qubits as LCR circuits ranks chip layouts from Monte Carlo infidelity distributions.","key_machinery":"The machinery is a lumped-element LCR model of the dispersive-readout measurement chain, combined with a peak-width-to-lifetime mapping. Each transmon is described by $L_q = 1/(C_q\\omega_q^2)$ and $R_q = T_1^{(q)}/C_q$, each tank circuit by $L_r = 1/(C_r\\omega_r^2)$, and the coupling strength is $g/2\\pi = (1/2)(C_g/\\sqrt{C_q C_r})\\sqrt{\\omega_q\\omega_r}$. The load-bearing object is the transmission spectrum: SPICE computes the output voltage versus frequency, and the full width of the qubit/resonator peak $\\delta\\omega_p$ is interpreted as the inverse relaxation rate $\\Gamma_1 = 1/\\delta\\omega_p$. This single mapping is what turns an ordinary circuit solver into a fidelity estimator and is also the step that lets thousands of coupled oscillators be simulated as one large netlist.","core_discovery":"The central claim is that a completely classical circuit simulation can estimate readout fidelity for large superconducting qubit arrays. In the model, the transmon (a common superconducting qubit design) is replaced by $L_q$, $C_q$, $R_q$ elements, the tank circuit by its own $L_r$, $C_r$, $R_r$ elements, and qubit-resonator coupling by a capacitance $C_g$; the resistance $R_q$ is set by the input relaxation time through $R_q = T_1^{(q)}/C_q$. From the SPICE AC transmission spectrum the authors identify the resonance peak and read off its full width at half maximum $\\delta\\omega_p$, then set $\\Gamma_1 = 1/\\delta\\omega_p$ through $T_1^{(m)} = 1/\\delta\\omega_p$. Using $\\Gamma_2 \\approx 2\\Gamma_1$ and the fidelity expression Eq. (1), they obtain per-run infidelities; repeating with Gaussian parameter variations yields the distribution. The main quantitative findings are that the square readout structure gives considerably better infidelity than the linear structure at 1% variations, that infidelity distributions widen when variations grow from 1% to 3%, and that the $N$-dependent prefactor in Eq. (1) makes infidelity grow with qubit count even when the 1,000- and 10,000-qubit spectra look similar.","pith_inferences":["If the peak-width-to-$T_1$ mapping survives direct comparison with experiment, this SPICE pipeline could be coupled to cryogenic CMOS control-circuit models, giving a single classical toolchain for qubit and control-electronics co-design.","The fidelity estimate folds dephasing into relaxation through $\\Gamma_2 \\approx 2\\Gamma_1$; using an independently measured $\\Gamma_2$ would reveal whether that simplification biases the architecture ranking.","The absolute infidelity scale depends on the uncalibrated operating time $\\tau_{\\rm op}^{(0)}$; calibrating that parameter once with randomized benchmarking on a small device would let the same netlist extrapolate relative infidelity trends to much larger arrays.","The split peaks seen in the square structure suggest that avoided crossings in classical transmission spectra could be used as a diagnostic of qubit-qubit crosstalk, turning a source of error into a measurable design indicator."],"forward_implications":["A designer can screen a candidate qubit layout against fabrication tolerances before running full quantum simulations, since 1,000-qubit SPICE runs take minutes on a laptop.","The linear four-qubit readout structure is predicted to have considerably worse infidelity than the square structure under the same 1% parameter variations, giving an immediate architectural ranking.","Raising Gaussian parameter variations from 1% to 3% broadens the infidelity distribution, and transmission peaks from neighboring qubits can merge when the frequency spread approaches their 200 MHz spacing, so the method sets a tolerance budget on qubit frequency placement.","Because the prefactor in Eq. (1) grows with $N$, infidelity degrades as the array scales even when the raw spectra of 1,000 and 10,000 qubits look similar, meaning larger chips amplify per-qubit parameter errors.","Additional readout components such as mixers and amplifiers can be added to the same SPICE netlist, so the method extends naturally to a full measurement-chain assessment."],"supporting_citations":[{"why":"Introduces the SPICE-based LCR estimation of qubit relaxation time that this work extends to fidelity.","marker":"[16]"},{"why":"Defines the transmon qubit and its capacitance/energy parameters used to set LCR element values.","marker":"[17]"},{"why":"Provides the cavity-QED setup of qubits capacitively coupled to a transmission line, the architecture under study.","marker":"[18]"},{"why":"Gives the dispersive readout description of the qubit-resonator interaction used to define the measurement regime.","marker":"[19]"},{"why":"Supplies the density-matrix decoherence rates $\\Gamma_1$ and $\\Gamma_2$ that enter the fidelity formula.","marker":"[20]"},{"why":"Supplies the coupling-strength expression and the relation $T_1=C_qR_q$ used to fix the qubit resistance.","marker":"[21]"},{"why":"The SPICE engine whose AC analysis produced the transmission spectra and Monte Carlo data.","marker":"[32]"},{"why":"Provides the fidelity formula (Eq. 1) that converts relaxation and dephasing rates into readout fidelity.","marker":"[33]"}],"fun_headline_variants":["SPICE simulates 10k-qubit readout fidelity","Classical circuits, laptop SPICE: 10k qubit fidelity","Laptop SPICE predicts 10,000-qubit fidelity","10,000-qubit readout fidelity via SPICE","Readout fidelity for 10k qubits with SPICE circuits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument stands on equating the width of a classical transmission peak with the quantum relaxation rate ($\\Gamma_1 = 1/\\delta\\omega_p$), even though the circuit resistance that controls that width was itself chosen from the input $T_1$ via $R_q = T_1^{(q)}/C_q$; if the peak width merely reflects the input value, the fidelity numbers in Fig. 5 are not independent predictions.","fun_headline_variants_meta":{"raw":{"variants":["SPICE simulates 10k-qubit readout fidelity","Classical circuits, laptop SPICE: 10k qubit fidelity","Laptop SPICE predicts 10,000-qubit fidelity","10,000-qubit readout fidelity via SPICE","Readout fidelity for 10k qubits with SPICE circuits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001034,"raw_usage":{"total_tokens":4341,"prompt_tokens":923,"completion_tokens":3418,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":3330}},"tokens_in":539,"tokens_out":3418,"duration_ms":25271,"temperature":1.0,"reasoning_tokens":3330,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:49:27.485236+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a single transmon with a known, independently measured $T_1$, set $R_q = T_1/C_q$ in the SPICE model, extract $\\delta\\omega_p$ from the simulated transmission peak, and compare $1/\\delta\\omega_p$ with the input $T_1$; if the two disagree beyond numerical error, the peak-width mapping is invalid. The same check can be done in hardware by measuring the transmission peak width and the relaxation time of the same device and comparing them.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the SPICE-based LCR estimation of qubit relaxation time that this work extends to fidelity."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the transmon qubit and its capacitance/energy parameters used to set LCR element values."},{"cited_title":"Tanamoto, T","cited_arxiv_id":null,"evidence_quote":"Provides the cavity-QED setup of qubits capacitively coupled to a transmission line, the architecture under study."},{"cited_title":"Koch, T.M","cited_arxiv_id":null,"evidence_quote":"Gives the dispersive readout description of the qubit-resonator interaction used to define the measurement regime."},{"cited_title":"Wallraff, D","cited_arxiv_id":null,"evidence_quote":"Supplies the density-matrix decoherence rates $\\Gamma_1$ and $\\Gamma_2$ that enter the fidelity formula."},{"cited_title":"Blais, R.-S","cited_arxiv_id":null,"evidence_quote":"Supplies the coupling-strength expression and the relation $T_1=C_qR_q$ used to fix the qubit resistance."},{"cited_title":"Knill, D","cited_arxiv_id":null,"evidence_quote":"The SPICE engine whose AC analysis produced the transmission spectra and Monte Carlo data."},{"cited_title":"Ryan, M Laforest, and R Laflamme New J","cited_arxiv_id":null,"evidence_quote":"Provides the fidelity formula (Eq. 1) that converts relaxation and dephasing rates into readout fidelity."}],"review_version":2}