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arXiv:2607.05779

Separate Control of Transient Leakage Exposure and Endpoint Leakage in Fast Transmon Gates

Haoran Yang, Fudong Liu, Weilong Wang, Yangyang Fei, Zheng Shan

quant-phSubmitted Jul 7, 2026• Announced Jul 8, 2026• 0 citations• Revised Jul 16, 2026 (v2)
v1 · Jul 7, 2026v2 · Jul 16, 2026
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Abstract

Leakage to noncomputational states limits the speed of single-qubit gates in weakly anharmonic transmons. Conventional pulse-shaping methods, including derivative removal by adiabatic gate (DRAG), primarily suppress the leakage remaining at the end of a gate. Here we demonstrate that endpoint leakage and the transient leakage population that accumulates during the gate represent distinct control objectives. Endpoint leakage is associated with the drive spectrum at the anharmonicity, whereas transient exposure depends on spectral weight over a finite frequency band and governs the additional leakage induced by dephasing. A spectral null at the leakage transition therefore suppresses the endpoint amplitude without necessarily reducing transient exposure. Based on this distinction, we introduce a path--endpoint separation pulse that combines transient-path shaping with a two-tone endpoint correction. For a $10$ ns $R_X(π/2)$ gate with an anharmonicity magnitude of $0.2$ GHz, numerical simulations show a $21\%$ reduction in transient exposure relative to cosine DRAG and a corresponding $20\%$ reduction in dephasing-induced excess leakage. The two correction tones further suppress residual leakage through the $|2\rangle$ and $|3\rangle$ channels, lowering the coherent endpoint leakage from approximately $7\times10^{-7}$ to $3\times10^{-8}$ without increasing transient exposure. These results establish transient exposure and endpoint leakage as complementary targets for the design of fast transmon gates.

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Leakage to noncomputational states limits the speed of single-qubit gates in weakly anharmonic transmons. Conventional pulse-shaping methods, including derivative removal by adiabatic gate (DRAG), primarily suppress the leakage remaining at the end of a gate. Here we demonstrate that endpoint leakage and the transient leakage population that accumulates during the gate represent distinct control objectives. Endpoint leakage is associated with the drive spectrum at the anharmonicity, whereas transient exposure depends on spectral weight over a finite frequency band and governs the additional leakage induced by dephasing. A spectral null at the leakage transition therefore suppresses the endpoint amplitude without necessarily reducing transient exposure. Based on this distinction, we introduce a path--endpoint separation pulse that combines transient-path shaping with a two-tone endpoint correction. For a 101010 ns RX(π/2)R_X(π/2)RX​(π/2) gate with an anharmonicity magnitude of 0.20.20.2 GHz, numerical simulations show a 21%21\%21% reduction in transient exposure relative to cosine DRAG and a corresponding 20%20\%20% reduction in dephasing-induced excess leakage. The two correction tones further suppress residual leakage through the ∣2⟩|2\rangle∣2⟩ and ∣3⟩|3\rangle∣3⟩ channels, lowering the coherent endpoint leakage from approximately 7×10−77\times10^{-7}7×10−7 to 3×10−83\times10^{-8}3×10−8 without increasing transient exposure. These results establish transient exposure and endpoint leakage as complementary targets for the design of fast transmon gates.
Improving the speed and fidelity of quantum logic gates is essential to reach quantum advantage with future quantum computers. However, fast logic gates lead to increased leakage errors in superconducting quantum processors based on qubits with low anharmonicity, such as transmons. To reduce leakage errors, we propose and experimentally demonstrate two new analytical methods, Fourier ansatz spectrum tuning derivative removal by adiabatic gate (FAST DRAG) and higher-derivative (HD) DRAG, both of which enable shaping single-qubit control pulses in the frequency domain to achieve stronger suppression of leakage transitions compared to previously demonstrated pulse shapes. Using the new methods to suppress the e f transition of a transmon qubit with an anharmonicity of − 212 MHz, we implement R X ( π / 2 ) gates achieving a leakage error below 3.0 × 10 − 5 down to a gate duration of 6.25 ns without the need for iterative closed-loop optimization. The obtained leakage error represents a 20-fold reduction in leakage compared to a conventional cosine DRAG pulse. Employing the FAST DRAG method, we further achieve an error per gate of ( 1.56 ± 0.07 ) × 10 − 4 at a 7.9-ns gate duration, outperforming conventional pulse shapes both in terms of error and gate speed. Furthermore, we study error-amplifying measurements for the characterization of temporal microwave control-pulse distortions, and demonstrate that non-Markovian coherent errors caused by such distortions may be a significant source of error for sub-10-ns single-qubit gates unless corrected using predistortion. Published by the American Physical Society 2024
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A flat-top transmon pulse with cosine ramps is shown to possess exact spectral zeros at half-integer values of the product of ramp duration and anharmonicity, τ | α | = n + 1/2, and these zeros are shown to predict the positions of endpoint-leakage minima in the weak-drive regime. Dimensionless adiabaticity measures are widely used to characterise driven quantum systems; when such a measure is used as a scan coordinate its independence from the remaining pulse parameters must first be established. Within any self-similar one-scale envelope family Ω ( t ) = Ω ₀ f ( t / σ ) the non-adiabaticity parameter is exactly degenerate with pulse area, η ref · θ = C shape , so an independent ramp timescale τ is introduced to remove the degeneracy. The Fourier amplitude of the resulting envelope at the anharmonicity vanishes identically when τ | α | = n + 1/2, which is destructive interference between the contributions of the rising and falling edges; the cancellation is independent of the plateau length and therefore of the total pulse duration. The link to the dynamics is perturbative: to leading order the endpoint-leakage amplitude is set by the Fourier component of the product of the envelope and the instantaneous excited-state amplitude, which removes a second, plateau-derived family of envelope zeros that the dynamics does not follow. Four-level Duffing simulations with parameters representative of IBM Heron r2 devices collapse the minima onto the sequence at six total pulse durations from 50 to 100 ns with a root mean-square deviation of 0.034 in units of τ | α |; for the four durations resolved on a finer grid, inclusion of the first-order population weighting reduces the positional deviation from 0.0234 to 0.0096. The competing plateau condition does not collapse the data. The residual displacement from the half-integers persists in the weak-drive limit and is set by the population-weighted pulse geometry rather than by drive amplitude. The simulations follow the weak-drive sequence for Ω /| α | ≤ 0.05 over the range tested; additional minima appear at stronger drive. The paper presents only a weak-drive analytical result and its four-level Duffing numerical verification. The hardware measurements on two IBM Heron r2 processors are used only for drive-amplitude calibration, and no gate fidelity, randomized benchmarking, process tomography, or hardware measurement of the leakage minima is claimed.
Simple analytic pulse-shaping techniques are of great practical utility in quantum control, with prime examples being the DRAG method for suppressing leakage in superconducting microwave gates and the transitionless-driving approach to shortcuts-to-adiabaticity. Standard versions of these methods require two orthogonal control channels, with the second channel effectively breaking time-reversal symmetry. This appears to rule out their use in settings with only a single real-valued control field, such as the kind of baseband flux control that is common in many superconducting circuit architectures. We show here that a simple analytic pulse-shaping technique derived via a Magnus expansion is effective even with just a single baseband control channel. We demonstrate its efficacy by simulating a two-qubit gate between transmons realized with a tunable coupler and baseband flux pulses. Our corrections dramatically reduce non-adiabatic leakage caused by ramping the coupler: for realistic device parameters, leakage in a fast iSWAP gate is suppressed by up to three orders of magnitude. Our approach is general, goes beyond simply suppressing unwanted spectral weight at leakage transitions, and can be applied to a variety of platforms.
The ability to perform fast and accurate rotations between the computational basis states of quantum bits is one of the most fundamental requirements for building a quantum computer. Because physical qubits generally contain more than two levels, faster gates often result in a higher leakage rate outside of the computational space. In this Letter, we enhance the state-of-the-art single qubit gate by introducing active leakage cancellation. This is accomplished via a second drive tone near the leakage transition such that we cancel the leakage caused by the main drive. Furthermore, we describe a measurement sequence that can be used to calibrate the parameters of this leakage cancellation drive. Finally, we apply the technique to superconducting transmon qubits and achieve leakage suppression by up to a factor of 20 when compared to pulses shaped with the standard derivative removal by adiabatic gate technique. This results in a coherence-limited gate infidelity of 7.5×10^{-5} with leakage below 10^{-5} level, for a 10 ns π/2 gate and 196 MHz qubit anharmonicity.
One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below 2.0×10−52.0\times10^{-5}2.0×10−5, and obtain fidelities above 99.98%99.98\%99.98% for pulse durations down to 6.8 ns for both XXX and X/2X/2X/2 gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below 10−610^{-6}10−6. The presented approach can be readily applied to other qubit types as well.