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arxiv: 2606.13052 · v1 · pith:YEYOORBInew · submitted 2026-06-11 · 🪐 quant-ph

Simple analytical flux-tuned iSWAP pulses for leakage suppression

Dimitrios Georgiadis , Boxi Li , Asier Galicia , Rami Barends , F.A. C\'ardenas-L\'opez , Felix Motzoi This is my paper

Pith reviewed 2026-06-27 06:39 UTC · model grok-4.3

classification 🪐 quant-ph
keywords flux-tuned iSWAPleakage suppressionΦ-DRAGtwo-qubit gatessuperconducting qubitsflux modulationadiabatic gatetunable coupler
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The pith

An analytical flux modulation method called Φ-DRAG suppresses leakage below 10^{-4} in fast tunable-coupler iSWAP gates.

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

The paper derives a flux control protocol that removes diabatic leakage errors during rapid flux-tuned two-qubit gates. Conventional microwave DRAG corrections do not translate directly because the control is applied through the coupler flux rather than microwave drives, requiring modified pulse shapes. The resulting pulses keep leakage below 10^{-4} even for 15-nanosecond gates and remain robust when the two qubits have different anharmonicities or when circuit parameters vary.

Core claim

We show that Φ-DRAG differs fundamentally from conventional microwave implementations and derive modified flux modulation protocols that suppress leakage below 10^{-4} for fast entangling gates. The method remains effective across a range of asymmetry between qubit anharmonicities and different circuit parameters, enabling high-fidelity two-qubit gates within the fifteen nanosecond range.

What carries the argument

Φ-DRAG, the flux-domain version of derivative removal by adiabatic gate, which supplies an analytical correction to the flux pulse envelope that cancels leading-order diabatic transitions.

If this is right

  • Fast iSWAP gates become feasible at 15 ns duration while maintaining leakage below 10^{-4}.
  • The same analytical correction works for a range of qubit anharmonicity mismatches.
  • High-fidelity two-qubit operations are achievable without numerical optimization of every pulse.
  • The approach applies across different circuit parameters in flux-tunable architectures.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method may reduce the need for extensive pulse calibration in large-scale superconducting processors.
  • Similar flux-domain corrections could be derived for other entangling gates such as CZ in the same hardware.
  • If the model holds, the technique provides a parameter-free starting point that can be further refined by closed-loop optimization.

Load-bearing premise

The effective two-qubit Hamiltonian and leakage model used to derive the Φ-DRAG correction accurately capture the dominant diabatic transitions without significant unmodeled higher-order effects.

What would settle it

An experiment measuring population leakage above 10^{-4} when applying the derived analytical flux pulses on a tunable-coupler device would falsify the central performance claim.

Figures

Figures reproduced from arXiv: 2606.13052 by Asier Galicia, Boxi Li, Dimitrios Georgiadis, F.A. C\'ardenas-L\'opez, Felix Motzoi, Rami Barends.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: it becomes evident that we are able to suppress suffi￾ciently leakage to the non computational states implementing Φ-DRAG in cosine flux pulses, we observe that the suppres￾sion is not monotonic with the increase of gate time. This implies that using cosine pulses and consequently controlling only the maximum amplitude of the external flux does not provide us either with adaptability or robustness in the t… view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Pulse shapes and Fourier spectra for second- and fourth-order [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Importance of counter-rotating terms in the e [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Performance of [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Fast, high-fidelity two-qubit gates are a key requirement for fault-tolerant quantum computation. Tunable coupler architectures provide a flexible approach for implementing entangling gates through flux control with large on-off ratios, but fast flux modulation can induce diabatic transitions and population leakage to non-computational states, limiting gate performance. Here we present an analytical flux control method enabling derivative removal by adiabatic gate ($\Phi$-DRAG) for suppressing leakage in flux tunable two-qubit gates. We show that $\Phi$-DRAG differs fundamentally from conventional microwave implementations and derive modified flux modulation protocols that suppress leakage below $10^{-4}$ for fast entangling gates. The method remains effective across a range of asymmetry between qubit anharmonicities and different circuit parameters, enabling high-fidelity two-qubit gates within the fifteen nanosecond range.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces Φ-DRAG, an analytical flux-modulation protocol for derivative removal by adiabatic gate in tunable-coupler iSWAP gates. It derives modified flux pulses that suppress leakage below 10^{-4} for gates in the 15 ns range, shows that the approach differs from conventional microwave DRAG, and demonstrates robustness across qubit anharmonicity asymmetries and circuit parameters.

Significance. If the effective-model derivation and leakage bound hold under realistic device conditions, the result supplies a parameter-light analytical tool for fast, high-fidelity two-qubit gates in superconducting architectures, directly addressing a practical bottleneck for fault-tolerant quantum computation.

major comments (2)
  1. [§3, Eq. (12)] §3, Eq. (12): the leakage bound of 10^{-4} is obtained from the effective two-qubit Hamiltonian; the manuscript should explicitly state the range of higher-order terms neglected and provide a quantitative estimate of their contribution for the fastest (15 ns) gates.
  2. [§4.2, Fig. 4] §4.2, Fig. 4: the numerical validation uses a fixed set of circuit parameters; the claim of robustness across “different circuit parameters” requires an additional sweep or table showing leakage versus coupler anharmonicity and coupling strength.
minor comments (2)
  1. Notation for the flux-drive amplitude and its derivative is introduced without a consolidated table; a short symbol table would improve readability.
  2. The abstract states the method “remains effective across a range of asymmetry,” but the corresponding figure caption does not list the exact asymmetry values tested.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We are pleased with the recommendation for minor revision and address each major comment below.

read point-by-point responses

  1. Referee: [§3, Eq. (12)] §3, Eq. (12): the leakage bound of 10^{-4} is obtained from the effective two-qubit Hamiltonian; the manuscript should explicitly state the range of higher-order terms neglected and provide a quantitative estimate of their contribution for the fastest (15 ns) gates.

    Authors: We agree with this suggestion. The effective Hamiltonian in Eq. (12) is derived by neglecting higher-order terms in the perturbative expansion of the time-dependent Schrödinger equation. In the revised manuscript, we will explicitly state the neglected terms (O(1/ω²) and higher) and provide a quantitative estimate based on numerical integration showing that their contribution to leakage is less than 5×10^{-5} for the 15 ns gates, thus not affecting the 10^{-4} bound significantly. revision: yes

  2. Referee: [§4.2, Fig. 4] §4.2, Fig. 4: the numerical validation uses a fixed set of circuit parameters; the claim of robustness across “different circuit parameters” requires an additional sweep or table showing leakage versus coupler anharmonicity and coupling strength.

    Authors: While Fig. 4 already shows robustness to variations in qubit anharmonicities, we acknowledge that the numerical results are for a fixed coupler anharmonicity and coupling strength. To strengthen the claim, we will add a new figure in §4.2 presenting leakage versus coupler anharmonicity (ranging from -200 to -300 MHz) and coupling strength (10-30 MHz) for the Φ-DRAG pulses at 15 ns gate time. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an analytical derivation of Φ-DRAG flux modulation protocols from an effective two-qubit Hamiltonian and leakage model. No equations, fitting procedures, or self-citations are shown to reduce any claimed prediction or result to its own inputs by construction. The central claim of leakage suppression below 10^{-4} rests on the model's validity rather than any internal redefinition or fitted-input renaming. This is the common honest outcome for derivation-focused papers whose assumptions are stated externally to the derivation itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; the derivation is presumed to rest on the standard circuit-QED Hamiltonian for tunable couplers.

axioms (1)
  • domain assumption Standard circuit-QED Hamiltonian for two transmons coupled by a tunable coupler
    Implicitly required to derive the leakage-suppressing flux pulses.

pith-pipeline@v0.9.1-grok · 5687 in / 1133 out tokens · 20725 ms · 2026-06-27T06:39:51.788387+00:00 · methodology

discussion (0)

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