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REVIEW 4 major objections 5 minor 42 references

Construction of new type of CNOT gate using cross-resonance pulse in the transmon-PPQ system

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Pith's one-line read This paper claims that a cross-resonance microwave pulse on a tunable transmon, followed by an auxiliary pulse and virtual Z rotations, implements a CNOT gate with a parity-protected qubit coupled through a resonator at 0.9989 average…

desk verdict A plausible but idealized numerical proposal for a CR-based CNOT in a transmon-PPQ hybrid; the 0.9989 fidelity is an optimized closed-system number, so the practical claims outrun the evidence. read the letter →

arxiv 2501.15218 v3 pith:KCREO6SE submitted 2025-01-25 quant-ph

Jeongsoo Kang , Younghun Kwon This is my paper · ORCID
classification quant-ph
keywords cross-resonancegateparity-protectedqubittransmonCNOTsuperconductinghybridsystemquantumfidelityresonatorcouplermicrowavepulse
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

Parity-protected superconducting qubits (PPQs) can hold quantum information longer than transmons, but no efficient way to entangle them had been shown. This paper claims that a CNOT gate can be made by coupling a tunable transmon and a PPQ through a resonator and driving the transmon with a cross-resonance microwave pulse near the PPQ frequency, then applying a short auxiliary pulse to the PPQ and virtual Z rotations. It gives concrete hardware specifications and optimized pulse parameters (Table I) and reports an average gate fidelity of 0.9989 from a full multi-level simulation. If correct, hybrid transmon–PPQ processors could be controlled with the same microwave drive lines already used for transmons, while gaining the PPQ's longer coherence.

What carries the argument

The carrying mechanism is the cross-resonance (CR) drive: a microwave pulse applied to the control qubit at the target qubit's frequency, which produces a conditional rotation of the target whose sign depends on the control state. In this hybrid system the drive acts on the transmon, the PPQ is the target, and a resonator with frequency $\omega_R = 2\pi \times 2.4$ GHz mediates the interaction; the Hamiltonian couples the resonator to both qubits capacitively with strength $G = 2\pi \times 0.01$ GHz. Because the transmon tunnels single Cooper pairs ($\cos\hat\phi_T$) while the PPQ tunnels pairs ($\cos 2\hat\phi_P$), the two have very different spectra, so the pulse parameters in Table I—CR frequency $f_1 = 2.8470$ GHz near the PPQ frequency, auxiliary pulse at $f_2 = 2.8472$ GHz, and virtual Z rotations—are what make the CR effect produce a CNOT.

What would settle it

Take the same pulse parameters from Table I and run the simulation with Lindblad dissipators or measured $T_1$ and $T_2$ rates for both qubits, or perform randomized benchmarking on a fabricated device. If the average gate fidelity drops materially below 0.9989, the practical claim that this gate is almost sufficient for error suppression would not hold.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the cross-resonance effect—normally used between two similar fixed-frequency qubits—still works when the control is a transmon and the target is a parity-protected Cooper-pair qubit, provided the system parameters and pulse shapes are chosen together. The PPQ's computational states are two same-parity plasmon levels, and the gate sequence is $\mathrm{CNOT}_{TP} = \hat{Z}\,\hat{U}_{\mathrm{Aux}}\,\hat{U}_{\mathrm{CR}}$: first the CR pulse on the transmon, then a single-qubit rotation on the PPQ whose phase $\gamma_2$ is tuned to cancel the leftover conditional rotation, and finally virtual Z gates. The simulation includes four levels for each device and the resonator, and reports an average fidelity of $0.9989$, with near-zero relative phases of the four basis outputs.

Load-bearing premise

The load-bearing premise is that the entire transmon–PPQ–resonator system evolves as a closed, decoherence-free quantum system throughout the pulse sequence, so the quoted 0.9989 fidelity contains no contribution from energy relaxation, dephasing, or environmental noise.

Editorial extensions

If this is right

  • The transmon–PPQ hybrid can use microwave-only control: no flux pulse is needed during the gate, so the PPQ's parity protection is not compromised during operation.
  • The optimization protocol yields a complete set of hardware and pulse parameters (resonator, energies, coupling, frequencies, durations) that can be used directly to simulate or build the gate.
  • CNOT gate fidelity of 0.9989 in a multi-level simulation brings the hybrid system close to the regime where quantum error correction could suppress residual errors.
  • Because the same-parity PPQ levels are driven by ordinary Rabi oscillations, single-qubit gates on the PPQ remain simple, so the hybrid device is compatible with standard transmon control stacks.

Reading between the lines

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

  • A master-equation simulation that adds relaxation, dephasing, charge and flux noise, and drive-amplitude errors—none of which appear in Eq. (1)—would likely lower the 0.9989 fidelity; the practical threshold claim depends on how much.
  • The same construction might extend to other protected or low-frequency superconducting qubits coupled through a resonator, since the CR drive only requires a well-chosen detuning between control frequency and target transition.
  • A natural experimental test is randomized benchmarking on a fabricated transmon–PPQ device; comparing the measured average fidelity with 0.9989 under the same pulse parameters would directly check the simulation.
  • The paper demonstrates the gate only with the transmon as control and PPQ as target; reversing the roles would require a separate pulse search and is not implied by the present results.
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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

4 major / 5 minor

Summary. The paper proposes a microwave-only CNOT gate in a hybrid superconducting system consisting of a tunable transmon and a parity-protected qubit (PPQ) coupled through a resonator. The protocol applies a cross-resonance (CR) pulse to the transmon (control), an auxiliary Gaussian pulse to the PPQ (target), and virtual Z rotations, with the total operation expressed as CNOT_TP = Z * U_Aux * U_CR in Eq. (10). The authors specify hardware parameters in Eqs. (1)-(6), provide optimized pulse parameters in Table I, and report an average gate fidelity of 0.9989 obtained from unitary Schrödinger evolution. They conclude that the gate is almost sufficient for error suppression and that the transmon-PPQ system is a promising building block for quantum computing.

Significance. If the numerical result survives more realistic modeling, the paper would be a useful contribution toward integrating parity-protected qubits with standard transmon control techniques, adding a CR-based CNOT to a hybrid platform. The manuscript is transparent about the Hamiltonian model, the Hilbert-space truncation, the pulse envelopes, and the optimization reference, which aids reproducibility. The main strength is a concrete, falsifiable specification of hardware and pulse parameters for a two-qubit gate. However, the headline fidelity is an idealized, optimized closed-system number; its relevance to the practical error-suppression claim depends on open-system effects that are not modeled, so the practical significance is currently overstated.

major comments (4)
  1. [Table I, Eq. (10), and Conclusion] The reported average fidelity of 0.9989 is computed from the closed-system unitary evolution of Eqs. (1)-(6), which contains no dissipation, dephasing, resonator decay, or drive-amplitude noise. Because the CR pulse duration is T1 = 1460 ns (Table I), comparable to or longer than typical transmon T1/T2 and resonator lifetimes, the conclusion that the gate is 'almost sufficient for error suppression' is not supported. Please add a Lindblad master-equation simulation with realistic T1, T2, and resonator kappa at the quoted hardware parameters, and report the resulting fidelity.
  2. [Eq. (5) and the paragraph defining H] The four-level truncation per subsystem is asserted to be 'sufficient to simulate the CR effect,' but no convergence test is presented. The CR effect is known to involve higher transmon levels (ref [36]), and the long CR pulse may populate the second and third excited states. Please provide a truncation-convergence test (e.g., 5 or 6 levels per subsystem) and report the residual leakage populations in the computational basis after the gate.
  3. [Table I and optimization description] The pulse parameters in Table I were optimized with Nelder-Mead (ref [40]) against the same unitary simulation used to compute the fidelity, so 0.9989 is a fit outcome rather than an independent prediction. Please state the cost function being optimized, the optimization bounds, and the sensitivity of the fidelity to each parameter, e.g., by perturbing f1, Omega_S, and T1 by small amounts and reporting the resulting fidelity changes.
  4. [Fidelity definition and Figure 3(a)] The fidelity measure is not specified: the text cites Nielsen's formula (ref [41]) but does not state whether the average is taken over the uniform Haar measure, a unitary 2-design, or the computational basis states only. Figure 3(a) shows only the four basis states. Please state the exact fidelity measure and report the standard deviation or the minimum fidelity over the sampled states.
minor comments (5)
  1. [Eq. (7)] The index i in {T, P} is introduced, but the pulse frequencies f_k and phases gamma_k are not labeled with the qubit index; please clarify which parameters belong to the transmon and PPQ pulses.
  2. [Notation] The subscript in CNOT_TP is used without definition; please define it as the control-target ordering (transmon control, PPQ target).
  3. [Abstract and Introduction] The statement that the PPQ shows 'better coherence performance' is not quantified; please provide the relevant coherence times or cite the specific experimental values from refs [12,13].
  4. [Eq. (5)] The resonator is truncated to Fock states k in {0,1,2,3}, but the justification for this truncation is not given; the resonator may be excited during the CR pulse, so its truncation should also be validated.
  5. [Figure 3(a) caption] The caption mentions state tomography, but the text does not describe the tomography procedure; please clarify whether this is full quantum state tomography or a population measurement.

Circularity Check

0 steps flagged · score 0.0 of 10

No material circularity: the reported 0.9989 CNOT fidelity is an optimized simulation result, not a prediction derived from the target gate.

full rationale

The derivation chain is: (i) define the transmon-PPQ-resonator Hamiltonian in Eqs. (1)-(4); (ii) truncate to four levels per subsystem, Eq. (5), with computational basis Eq. (6); (iii) choose pulse ansatze in Eqs. (7)-(9), including the CR pulse and auxiliary Gaussian pulse; (iv) optimize the pulse parameters with Nelder-Mead (Ref. [40]) against the CNOT target, as described in the text around Eq. (10) and Table I; and (v) report the resulting average fidelity F = 0.9989. The CNOT target enters only through the cost function used to select pulse parameters; it is not substituted into the Hamiltonian or into the Nielsen average-fidelity formula. The time evolution and the fidelity calculation are therefore independent of the target gate, so the result is a constructive numerical design rather than a circular derivation. The main caveats are non-circular limitations: the simulation is closed-system unitary with no Lindblad dissipation or dephasing, so the quoted fidelity is an idealized number; the sufficiency of the four-level truncation is asserted but not demonstrated with convergence or leakage-population data; and the conclusion that the gate is 'almost sufficient for error suppression' goes beyond what a noiseless simulation can establish. The self-citation in Ref. [23] is used only as a design reference for the coupling strength and is not load-bearing. No step in the paper reduces, by construction or by self-citation, to its own input.

Assumptions & free parameters 12 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the chosen PPQ model, the four-level truncation, the transferability of cross-resonance to the heterogeneous pair, and the neglect of decoherence. The pulse and hardware parameters are hand-chosen or optimized, not derived from first principles.

free parameters (12)
  • f1 = 2.8470 GHz
    CR pulse carrier frequency, tuned near the PPQ transition; optimized to maximize CNOT fidelity.
  • f2 = 2.8472 GHz
    Auxiliary pulse frequency, set near the PPQ frequency; optimized.
  • T1 = 1460.0 ns
    Plateau duration of the CR pulse; optimized.
  • T2 = 9.9966 ns
    Duration of the auxiliary Gaussian pulse; optimized.
  • Omega_S = 0.03000
    Amplitude of the CR pulse; optimized.
  • Omega_G = 0.02078
    Amplitude of the auxiliary pulse; optimized.
  • rho = 0.09986
    Rising-time ratio for the sinusoidal flat-top envelope; optimized.
  • gamma_1 = -1.068e-06
    Initial phase of the CR pulse; optimized.
  • gamma_2 = 2.4186
    Initial phase of the auxiliary pulse; optimized.
  • theta_1 = 0.6007
    Virtual Z rotation angle on the transmon; optimized.
  • theta_2 = -0.0333
    Virtual Z rotation angle on the PPQ; optimized.
  • Hardware spectroscopy set = omega_R=2pi*2.4 GHz, E_C,T=E_C,P=2pi*0.2 GHz, E_J,Sigma,T=2pi*6 GHz, E_J,P=2pi*3 GHz, G=2pi*0.01 GHz, gamma=1.01
    Chosen by hand to create a viable frequency configuration for cross-resonance; not derived from first principles.
assumptions (5)
  • domain assumption The PPQ Hamiltonian Eq. (3) with cos(2*phi) and charge-offset drive correctly describes the parity-protected qubit.
    The PPQ is a proposed device [12,13]; the paper assumes this model and its selection rules without derivation.
  • domain assumption The two chosen PPQ states |mP=1> and |mP=2> (same parity, different plasmon modes) form a microwave-driven qubit with longer coherence than transmon states.
    The paper asserts these states can be driven by standard Rabi oscillation and retain long coherence, but no coherence times or drive matrix elements are computed.
  • ad hoc to paper Four-level truncation for resonator, transmon, and PPQ is sufficient to simulate the cross-resonance effect.
    The paper states 'the four lowest levels are sufficient' but provides no convergence check against larger truncations.
  • domain assumption Cross-resonance, established for two transmons, transfers to the heterogeneous transmon-PPQ pair.
    The central mechanism is assumed to work despite different qubit frequencies and selection rules; no effective Hamiltonian derivation is given.
  • domain assumption Closed-system unitary evolution without T1/T2 or noise represents the gate fidelity.
    Hamiltonian (1) has no dissipative terms, while the reported fidelity is presented as the gate fidelity.

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Pith. "Pith review of Construction of new type of CNOT gate using cross-resonance pulse in the transmon-PPQ system." pith.science (2026). https://pith.science/paper/KCREO6SE

@misc{pith2026250115218,
  author       = {Pith},
  title        = {Pith review of: Construction of new type of CNOT gate using cross-resonance pulse in the transmon-PPQ system},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KCREO6SE}},
  note         = {Machine review of arXiv:2501.15218}
}
read the original abstract

The transmon, known for its fast operation time and the coherence time of tens of microseconds, is the most commonly used qubit for superconducting quantum processors. However, it is still necessary to enhance the coherence time and the gate fidelity of superconducting quantum processors for the practical implementation of fault-tolerant quantum computing. Meanwhile, a novel superconducting qubit, which has the ability to protect the Cooper-pair parity on the superconducting island, has been proposed. This new qubit shows better coherence performance than the transmon, but it does not yet have an efficient method for realizing a superconducting hybrid system that harnesses it. In this work, we show how to implement a new type of CNOT gate in a superconducting hybrid system composed of tunable transmon and parity-protected qubit by applying a cross-resonance pulse. First, we provide hardware specifications and pulse parameters to construct a successful two-qubit gate in the hybrid system. Second, we show that our method can supply a CNOT gate of average fidelity with more than 0.998. Therefore, our work implies that the hybrid system may provide a new platform for quantum computers.

Figures

Figures reproduced from arXiv: 2501.15218 by the authors.

Figure 1
Figure 1. FIG. 1. Design of the transmon-PPQ system and eigenstates of the transmon and the PPQ, comprising the transmon-PPQ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The pulse protocol to implement CNOT [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Implementation and the trajectory of the Bloch vectors for the basis states after applying the CNOT [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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