Circuit simulation of readout process toward large-scale superconducting quantum circuits

Hiroshi Fuketa; Shiro Kawabata; Tetsufumi Tanamoto; Toyofumi Ishikawa

REVIEW 5 major objections 5 minor 36 references

Circuit simulation of readout process toward large-scale superconducting quantum circuits

T0 review · 5 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict Scalability and Monte Carlo variability are real, but the linewidth-to-T1 mapping is a load-bearing flaw that makes the reported fidelities uncalibrated. read the letter →

arxiv 2507.20100 v1 pith:23XBMOFA submitted 2025-07-27 quant-ph cond-mat.supr-con

Tetsufumi Tanamoto , Hiroshi Fuketa , Toyofumi Ishikawa , Shiro Kawabata This is my paper · ORCID

classification quant-phcond-mat.supr-con

keywords superconductingqubitstransmonreadoutfidelitySPICEsimulationLCRcircuitmodelfabricationvariabilitydispersiveMonteCarlo

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

The 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.

However, 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.

The 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.

If 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.

This 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.

Referee Report

5 major / 5 minor

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.

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 (5)

[Eq. (3) and the statement 'Here, we present the resonator peaks'] 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.
[Fidelity formula (1) and the role of tau_op] 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.
[Assumption Gamma2 approximately 2 Gamma1] 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.
[Eq. (1) prefactor and large-N behavior] 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.
[Fig. 5 and choice of tau_op] 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.

minor comments (5)

[Text around qubit parameters] 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.
[Fig. 4 caption] 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.
[Fig. 3 caption] 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.
[Reference list] 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.
[Eq. (4) notation] 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.

Circularity Check

2 steps flagged · score 6.0 of 10

The SPICE 'measured' Gamma1 is set by the input T1 through Rq, so the fidelity reduces to the assumed T1 times the free time tau_op.

fitted input called prediction [Sec. II (circuit model), Eqs. (3) and (1)]
"The dissipation is assumed to be described by the resistanceRq in the LCR circuits with the relationship T (q)1 = CqRq ... Rq = T (q)1 /Cq. ... T (m)1 ≡ 1 δωp . (3) The output peak of the transmission line was examined ... Subsequently, Γ 1 in Eq.(1) is given by Γ 1 = 1/T (m)1 ."

Rq is the only dissipative element and is fixed by the input T1^(q) via Rq = T1^(q)/Cq. The simulated peak width δωp is governed by that same Rq; for the underlying LCR resonance δωp = 1/(Rq Cq) = 1/T1^(q), so Eq. (3) returns T1^(m) = T1^(q). Inserting Γ1 = 1/T1^(m) into Eq. (1) makes the output fidelity a re-statement of the input T1^(q) (multiplied by the freely chosen tau_op), not an independent estimate. The paper itself takes T1^(q) 'as a given parameter for simplicity,' so the simulation cannot independently recover it; it can only return the input value or a circuit-determined multiple of it.
fitted input called prediction [Sec. II (after Eq. 1) and Sec. III (Fig. 5 discussion)]
"Here, we considerτ (0) op as an adjustment parameter, which should be determined experimentally in the future. ... Some ambiguity regarding the parameter τop is noted, and the values of the infidelities increase (decrease) as τop increases (decreases). Therefore, the absolute value of the infidelity should be determined experimentally. ... τiop = 10−11 s for (a)(b) and τiop = 10−12 s for (c)."

Eq. (1) is F = 1 − prefactor × tau_op × (Γ1+Γ2), with Γ1 obtained from Eq. (3). Since tau_op is a free adjustment parameter and Γ1 is set by the input T1, the absolute infidelity values in Fig. 5 are not derived predictions; they are the product of an assumed relaxation rate and an arbitrary time. The paper candidly admits this and restricts claims to relative values, but the relative comparison of linear vs square structures uses different tau_op values (10^-12 vs 10^-11), so even the relative comparison is partly an artifact of the chosen time constants.

full rationale

The computational scalability claim — that SPICE can handle 100, 1000, and 10000 qubits on a laptop — is an honest benchmark and is not circular; it stands independent of the physics of Eq. (3). The circularity is confined to the fidelity estimate. The derivation chain is: T1^(q) is an input parameter; Rq = T1^(q)/Cq sets the only dissipative element; SPICE computes a transmission peak width δωp; Eq. (3) converts δωp to T1^(m) and Γ1 = 1/T1^(m); Eq. (1) then multiplies Γ1 by the free time tau_op. For a single LCR resonance, δωp = 1/(Rq Cq) = 1/T1^(q), so the 'measured' lifetime equals the input value; for coupled resonators it is a circuit-dependent multiple of the input, but the scale remains set by the assumed T1. The fidelity is therefore not an independent prediction but a restatement of the input T1 times a freely chosen tau_op. The paper's statement that T1^(q) is a given parameter and that tau_op should be determined experimentally confirms this. Also, the paper states 'Here, we present the resonator peaks' when extracting the width for Eq. (3); in dispersive readout the resonator peak width is set by the cavity decay rate kappa rather than the qubit T1, which is a physical-validity risk rather than a circularity, but it reinforces that the Gamma1 values are unvalidated. The self-citation of Ref. 16 for Eq. (3) is load-bearing, but the reduction is visible in this paper's own equations, so the score reflects the in-paper circularity, not the citation alone. Overall: partial circularity, score 6.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central fidelity estimate rests on four main assumptions: validity of the classical LCR representation, validity of the cited fidelity formula, the linewidth-to-Gamma1 mapping, and the fixed ratio Gamma2=2*Gamma1. Two hand-set parameters, tau_op and T1^(q), control the output magnitude. No new physical entities or forces are introduced.

free parameters (2)

Operation time tau_op = 10^-11 s (square), 10^-12 s (linear)
Adjustable parameter in Eq. (1), described as needing experimental determination; absolute infidelity scales linearly with it.
Qubit relaxation time T1^(q) = 1 microsecond
Given input parameter set by hand for all qubits ('we take T1^(q) as a given parameter for simplicity'); it fixes Rq and therefore controls the simulated linewidth and Gamma1.

assumptions (5)

domain assumption Bloch-Redfield weak-coupling theory describes qubit decoherence with rates Gamma1 and Gamma2.
Invoked with Ref. 20 before Eq. (1); assumes weak coupling between qubit and environment.
domain assumption Transmon qubits and tank circuits can be represented as classical LCR circuits with Rq = T1^(q)/Cq.
Used throughout Figure 2 and the text; no derivation from a quantum circuit Hamiltonian is given.
ad hoc to paper The dephasing rate satisfies Gamma2 approximately 2*Gamma1.
Stated in the text without justification or experimental support; it is a specific noise assumption that is not generally true for transmon qubits.
domain assumption The fidelity formula from Abad et al., Eq. (1), applies to the readout process of this classical LCR model.
Eq. (1) is taken as a black box; no derivation or verification that this formula describes dispersive readout of N classical LCR qubits is provided.
domain assumption The transmission peak width delta_omega_p equals the inverse lifetime T1^(m), and Gamma1 = 1/T1^(m).
Stated near Eq. (3); this mapping from a classical circuit linewidth to a quantum relaxation rate is central to the fidelity estimate and is not validated.

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Cite this review

Pith. "Pith review of Circuit simulation of readout process toward large-scale superconducting quantum circuits." pith.science (2026). https://pith.science/paper/23XBMOFA

@misc{pith2026250720100,
  author       = {Pith},
  title        = {Pith review of: Circuit simulation of readout process toward large-scale superconducting quantum circuits},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/23XBMOFA}},
  note         = {Machine review of arXiv:2507.20100}
}

read the original abstract

The rapid scaling of superconducting quantum computers has highlighted the impact of device-level variability on overall circuit fidelity. In particular, fabrication-induced fluctuations in device parameters such as capacitance and Josephson critical current pose significant challenges to large-scale integration. We propose a simulation methodology for estimating qubit fidelity based on classical circuit simulation, using a conventional Simulation Program with Integrated Circuit Emphasis (SPICE) simulator. This approach enables the evaluation of the performance of superconducting quantum circuits with 10000 qubits on standard laptop computers. The proposed method provides an accessible tool for the early stage assessment of large-scale superconducting quantum circuit performance.

Figures

Figures reproduced from arXiv: 2507.20100 by the authors.

**Figure 2.** FIG. 2. Classical circuit models for the transmon system. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 1.** Fig.1. In the RB process, a series of single-qubit ro [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Examples of simulated transmission spectra of the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5. Infidelities calculated from Eq.(1) for (a) 1% vari [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

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2009

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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