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REVIEW 3 major objections 4 minor 49 references

Calibrating quantum gates up to 52 qubits in a superconducting processor

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper reports the largest quantum-gate fidelity benchmarks to date, reaching 52 qubits, and shows that optimizing a parallel gate with its global fidelity outperforms local optimization.

desk verdict Large-scale CAB benchmarking is real and worth referee time, but the 52-qubit fidelity inherits an unverified λ-sign assumption and the abstract oversells the optimization comparison. read the letter →

arxiv 2505.22390 v1 pith:RNFXK4XZ submitted 2025-05-28 quant-ph

Daojin Fan , Guoding Liu , Shaowei Li , Ming Gong , Dachao Wu , Yiming Zhang , Chen Zha , Fusheng Chen
show 13 more authors
Sirui Cao Yangsen Ye Qingling Zhu Chong Ying Shaojun Guo Haoran Qian Yulin Wu Hui Deng Gang Wu Cheng-Zhi Peng Xiongfeng Ma Xiaobo Zhu Jian-Wei Pan
This is my paper · ORCID
classification quant-ph
keywords quantumgatebenchmarkingcharacter-averageparallelCZgatescrosstalkcorrelationmetricZZcouplingnoisesuperconductingprocessoroptimization
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

The paper claims that a shallow-circuit protocol called character-average benchmarking (CAB) can deliver trustworthy process-fidelity estimates for very large parallel quantum gates, and it reports measurements on a 54-qubit superconducting processor for gates spanning up to 52 qubits. On a 44-qubit parallel controlled-Z (CZ) gate the measured fidelity is 63.09±0.23%, and on a 52-qubit parallel CZ gate the pure fidelity estimate is 38.92%. The authors also introduce a normalized correlation between the global gate fidelity and the product of its local gate fidelities, use it to detect crosstalk among parallel CZ gates, and show that optimizing with the global fidelity outperforms optimizing gate-by-gate: a 6-qubit parallel CZ gate improves from 87.65% to 92.04% while inter-gate correlation drops from 3.53% to 3.22%. If correct, the work offers a practical route to calibrating and optimizing the large multi-qubit gate layers needed in near-term quantum processors and quantum error-correction circuits.

What carries the argument

The central object is the quality parameter of the noise channel under Pauli twirling, estimated by fitting survival probabilities to $Aλ^{{2m}}$ for circuits of depth m. The protocol inserts random local Clifford and Pauli gates around alternating U and $U^{{-1}}$, then averages a constant number of sampled Pauli observables, so the classical postprocessing cost is independent of qubit number. The correlation metric is (F(U) − ∏F(U_i)) / √(F(U)∏F(U_i)), and the physical mechanism used to explain the data is a composite noise channel Λ = Λ_V ∘ ⊗_i Λ_{p_i}, where Λ_{p_i} is depolarizing and Λ_V is unitary ZZ coupling V = exp(−iΣ γ_{kl} Z_{i_k}Z_{i_l}).

What would settle it

Run CAB on the same 52-qubit parallel CZ gate with at least three circuit depths, such as m = 0, 1, 2, and 3, and inspect whether the fitted exponential decays all have positive amplitudes and consistent quality parameters; if any survival-probability curve can be fit equally well by a negative quality parameter, or if the fidelity estimate shifts by more than its error bars when depths are added, the near-depolarizing assumption fails for that gate.

Watch

Extended reading notes

Core claim

The paper demonstrates that character-average benchmarking can estimate the process fidelity of a Clifford gate on a shallow circuit whose depth does not scale with the gate's order. For a parallel CZ gate made of 22 independent CZ pairs on 44 qubits, it reports a purified fidelity of 63.09±0.23%; for the 26-pair blue pattern on 52 qubits, it reports a pure fidelity of 38.92%. The paper defines an inter-gate correlation as the normalized gap between the global fidelity and the product of local fidelities, detects positive and negative correlations consistent with pairwise ZZ couplings, and shows that using the global fidelity as the optimization target improves a 6-qubit parallel CZ gate from 87.65% to 92.04% while decreasing correlation from 3.53% to 3.22%.

Load-bearing premise

The extracted fidelity is trustworthy only if the noise on the gate is close to depolarizing, because the fitting procedure cannot tell a negative quality parameter from its positive mirror image.

Editorial extensions

If this is right

  • Large multi-qubit gate layers can be benchmarked end-to-end with shallow circuits, bypassing the exploding gate-order problem that blocks cycle benchmarking for fully connected gates.
  • The global fidelity of a parallel gate is a usable optimization target: on a 6-qubit, three-pair CZ gate it raises fidelity from 87.65% to 92.04% and lowers correlation from 3.53% to 3.22% relative to local-fidelity optimization.
  • Correlation values computed from the same experiment act as a crosstalk diagnostic: magnitudes track coupling strength, two-gate ZZ coupling gives positive correlation, and adding a strongly coupled third gate can flip the sign of the correlation.
  • Individual CZ fidelities in the orange pattern remain near 98% as the parallel gate grows, indicating weak short-range crosstalk, which the paper reads as favorable for quantum error correction.

Reading between the lines

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

  • Editorial extension: the 52-qubit blue-pattern fidelity should be read as conditional on near-depolarizing noise; the paper shows a quality-parameter distribution only for the orange pattern, so re-measuring the blue pattern with additional circuit depths would test whether all fitted quality parameters remain positive.
  • Editorial extension: the same correlation-versus-distance scatter analysis could be used to map the crosstalk graph of any qubit array and to decide where to place parallel gates to suppress correlated errors.
  • Editorial extension: the layer-by-layer decomposition of circuits, clustering strongly correlated gates and optimizing each cluster globally, is a concrete route to scale the method beyond six qubits; the paper suggests the idea but does not demonstrate it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports character-average benchmarking (CAB) measurements of large parallel CZ gates and of 'fully connected' gate layers on a 54-qubit superconducting processor. Using a constant number of sampled Z observables, the authors benchmark parallel CZ gates on up to 22 pairs (44 qubits) in one pattern and a 26-pair (52-qubit) gate in a second pattern, with a headline pure fidelity of 63.09%±0.23% for the 44-qubit gate. They define an inter-gate correlation metric from the same CAB data, observe positive short-range correlations in one pattern and some negative correlations in another, and explain the signs with a depolarizing-plus-ZZ-coupling noise model. They also use the global CAB fidelity as a cost function in Nelder-Mead optimization of 3-pair and 2-pair parallel CZ gates, reporting that global-fidelity optimization improves the 6-qubit gate from 87.65% to 92.04% while reducing the correlation from 3.53% to 3.22%, compared with local-fidelity optimization.

Significance. If the results hold, this is a substantial experimental scaling demonstration: CAB with constant sample complexity is used to estimate process fidelities for gates substantially larger than previous cycle-benchmarking demonstrations, and the correlation metric provides a practical crosstalk diagnostic from the same data. The paper includes a direct CAB-versus-cycle-benchmarking validation on three CZ gates, repeated-experiment standard deviations, and an error-propagation analysis of the reported uncertainties; these are genuine strengths. The ZZ-coupling model is simple enough to make falsifiable predictions (positive correlations for two-gate coupling, sign reversal when a third gate couples strongly), and the authors are explicit about the λ sign ambiguity. However, the 52-qubit claim rests on a diagnostic that is not shown for that gate, and the optimization comparison uses a post hoc iteration window; both points need attention before the scaling claim is fully established.

major comments (3)
  1. [Methods, Box 1 step 6 / Eq. (4); Results, 'Fully connected gate benchmarking'; Supplemental Table III] The protocol fits each quality parameter to f_i(m)=Aλ_i^{2m}, so the data determine only |λ_i|. Replacing a negative true λ_i by |λ_i| in Eq. (4) inflates the reported fidelity, and the authors explicitly acknowledge this in the 'Fully connected gate benchmarking' paragraph. That paragraph argues that the near-depolarizing condition is met for the fully connected gate and for the orange-pattern parallel CZ gate, where quality-parameter distributions are shown. For the 52-qubit blue-pattern gate, however, Supplemental Table III reports only dressed/local/pure fidelities and no quality-parameter distribution, so positivity is not established for exactly the gate that supports the 'up to 52 qubits' claim. Given the reported pure fidelity of 38.92%, the authors' own ZZ-coupling model (Eq. (15)) with γ ≳ π/4 can drive individual Pauli eigenvalues negative. The same concern applies to the blue-pattern correlation signs (Fig. 3(d)), since those correlations are computed from the same fidelity estimates. Please add the λ_i distributions for the blue pattern and an independent sign check, or restrict the headline claim to the 44-qubit orange pattern where the diagnostic is provided.
  2. ['Parallel CZ gate optimization', Figure 4, Supplemental Tables V and VI] The quantitative comparison in the abstract—87.65% to 92.04% and 3.53% to 3.22%—is computed from iterations 100–180, a range that the manuscript states was chosen because it is the 'phase of iterative parameter convergence and stable reference fidelities' (Figure 4 caption; see also Supplement Section II.E). This is a post hoc selection: the same data set was used to identify the stable phase and to estimate the improvement. The conclusion that global-fidelity optimization outperforms local-fidelity optimization should be supported by a pre-specified selection rule (for example, the last K iterations or an explicit convergence criterion applied identically to both runs), or by full optimization curves showing that the comparison is insensitive to the chosen window. As written, the headline optimization gain could be an artifact of the chosen window rather than of the objective function.
  3. [Supplemental Table III and Supplement Section II.B; 'Parallel CZ gate benchmarking'] For the 52-qubit blue-pattern gate, the dressed and local twirling fidelities are each estimated from two circuit depths only ({0,1} and {1,2}, respectively). With two points the exponential fit is exact and provides no goodness-of-fit check of the assumed Aλ^{2m} form, nor any estimate of model error. The supplement itself notes that with two survival probabilities 'there will be no fitting error'; this means the reported standard error reflects only measurement propagation, not the validity of the noise model. This is especially important because the 52-qubit gate is in the low-fidelity regime where the noise is not demonstrated to be close to depolarizing. Please include an additional depth, or repeated depth sets, for at least a sub-system or the full 52-qubit gate, and report the resulting stability of the fidelity and of the correlation values.
minor comments (4)
  1. [Introduction] The citation '[28? , 29]' contains an unresolved placeholder and should be replaced with the actual reference.
  2. [Results, 'Fully connected gate benchmarking'] The name 'fully connected gate' is potentially misleading for a brickwork layer of CZ gates on a ring; please add a one-sentence definition or choose a less suggestive term.
  3. [Figure 3 caption] Please state precisely how 'distance between CZ gates' is counted when two qubit pairs are not connected by a single edge; the current phrase 'minimal line count' is ambiguous.
  4. [Methods, Eq. (5) and Box 1 step 6] The Hoeffding bound is stated for λ_i, but the experimental estimate obtained from the fit is the magnitude |λ_i|; please clarify whether the inequality applies to the signed quality parameter or to the estimated magnitude.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fidelity estimates are direct CAB measurements, the correlation metric is definitional, and the noise-model parameters are not fit to the predicted correlations.

full rationale

The paper's derivation chain is self-contained against external benchmarks. The gate fidelities are obtained by applying the published CAB protocol (Ref. [33]) and averaging fitted quality parameters (Box 1, Eq. (4)); this is the operational estimator, not a quantity that is equivalent to an input by construction. The acknowledged limitation that a negative quality parameter λ is indistinguishable from −λ in the fit f_i(m)=Aλ^{2m} is an identifiability/validity caveat about the estimator, not a circular reduction of the reported fidelity to the fit itself. The inter-gate correlation in Eq. (6) is an explicit definition from simultaneously measured global and local fidelities, so claiming that nonzero correlation indicates interaction is a definitional statement, not a derived prediction. The ZZ-coupling noise model (Eqs. (13)-(27)) uses coupling strengths γ_kl = g_kl t with t = 110 ns and g_kl from known physical couplings, rather than fitting the correlation values, so the model's predicted signs follow algebraically from Eq. (27) and are not imposed by the data. The main self-citation, Ref. [33] for CAB, is a published protocol from partly overlapping authors, but it is load-bearing only as an external method; the paper independently validates CAB against cycle benchmarking in Supplemental Section I, giving outside support. The 52-qubit blue-pattern fidelity is subject to the negative-λ identifiability assumption, but that is a correctness and robustness risk, not circularity. Thus the central claims are not circular.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central fidelity values are direct measurements from the CAB experiment and do not rest on fitted parameters. The only model parameter of note, the ZZ-coupling phase γkl, is estimated from independent physical knowledge of coupling strengths and gate time rather than fitted to the correlation data. The key imported assumptions are the validity of the CAB protocol from the authors' own Ref [33], the depolarizing-noise assumption for large gates, and the composite noise model used to interpret correlations.

free parameters (1)
  • ZZ-coupling phase γkl = ≈0.033 for isolated pairs, ≈0.1 for coupled pairs
    Estimated from physical coupling strengths and the 110 ns gate time; used in the composite noise model (Eq. 15) to predict correlation magnitudes and signs. The values are not fitted to the correlation data but are chosen based on the processor's known coupling parameters.
assumptions (4)
  • domain assumption CAB protocol correctly estimates the process fidelity of a Clifford gate
    The paper relies on Ref [33] for the CAB procedure and its guarantees. It validates CAB against cycle benchmarking on three small CZ gates (Supplement Fig. S1), but the validity at 52-qubit scale is assumed. Ref [33] shares authors with this paper.
  • domain assumption Noise of benchmarked gates is close to depolarizing, so all quality parameters are non-negative
    The exponential fit to Aλ^{2m} cannot distinguish λ from −λ. The paper states this limitation and provides quality-parameter distributions only for the orange-pattern gates. For the 52-qubit blue-pattern gate, the assumption is unverified.
  • ad hoc to paper Composite noise model: local depolarizing noise followed by a unitary ZZ-coupling evolution
    The model (Eqs. 9-15) is introduced to explain the observed correlation signs and the optimization behavior. It is a plausible physical model but is not derived from first principles and is matched qualitatively to the data rather than quantitatively fit.
  • standard math Interleaved randomized benchmarking formula (Eq. 3) separates target gate fidelity from twirling gate fidelity
    Standard result from Magesan et al. [22], used to extract the pure parallel CZ fidelity from dressed fidelity. This is a well-established formula.

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Pith. "Pith review of Calibrating quantum gates up to 52 qubits in a superconducting processor." pith.science (2026). https://pith.science/paper/RNFXK4XZ

@misc{pith2026250522390,
  author       = {Pith},
  title        = {Pith review of: Calibrating quantum gates up to 52 qubits in a superconducting processor},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RNFXK4XZ}},
  note         = {Machine review of arXiv:2505.22390}
}
abstract

Benchmarking large-scale quantum gates, typically involving multiple native two-qubit and singlequbit gates, is crucial in quantum computing. Global fidelity, encompassing information about intergate correlations, offers a comprehensive metric for evaluating and optimizing gate performance, unlike the fidelities of individual local native gates. In this work, utilizing the character-average benchmarking protocol implementable in a shallow circuit, we successfully benchmark gate fidelities up to 52 qubits. Notably, we achieved a fidelity of 63.09$\pm $0.23% for a 44-qubit parallel CZ gate. Utilizing the global fidelity of the parallel CZ gate, we explore the correlations among local CZ gates by introducing an inter-gate correlation metric, enabling one to simultaneously quantify crosstalk error when benchmarking gate fidelity. Finally, we apply our methods in gate optimization. By leveraging global fidelity for optimization, we enhance the fidelity of a 6-qubit parallel CZ gate from 87.65% to 92.04% and decrease the gate correlation from 3.53% to 3.22%, compared to local gate fidelitybased optimization. The experimental results align well with our established composite noise model, incorporating depolarizing and ZZ-coupling noises, and provide valuable insight into further study and mitigation of correlated noise.

Figures

Figures reproduced from arXiv: 2505.22390 by the authors.

Figure 1
Figure 1. (a), with ΛU and Λ′ U being the Pauli-twirled noise channels of U and U −1 , respectively. This approach yields the CAB fidelity of U, closely approximating U’s fidelity under physically reasonable conditions [33]. Hereafter, we refer to the CAB fidelity simply as the gate fidelity unless stated otherwise. While estimating all quality parameters for fidelity evaluation demands exponential resources, the number of qu… view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. (a) using two distinct colors. We first evaluate the fidelities of the gates within the orange pattern, consisting of 22 pairs of CZ gates aligned in the same physical direction. This benchmarking was conducted progressively, starting with 2 pairs of CZ gates and incrementally including more gates up to the full set of 22 pairs. Subsequently, we evaluate the gate correlations within the orange and the blue patterns.… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

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