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arXiv:2607.05779

Separating transient leakage exposure from endpoint cancellation in fast transmon single-qubit gates

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

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

Fast single-qubit gates on weakly anharmonic transmons are limited by leakage to noncomputational states, and standard mitigations such as DRAG (derivative removal by adiabatic gate) act on the leakage amplitude at the end of the gate. We show that this endpoint amplitude and the transient leakage exposure accumulated during the gate are two distinct control objectives that can be assigned to separate modules. The endpoint is a single sample of the drive spectrum, $|\tildeΛ(η)|^2$; the exposure is a band integral about $η$ and governs leakage under dephasing, and the spectral-null condition $\tildeΛ(η)=0$ constrains only the former. We realize this split in a path--endpoint separation pulse (PESP): a path-shaping pulse suppresses the exposure, and a two-tone endpoint-cancellation pulse cancels the residual amplitude. For a $10$ ns $R_{X}(π/2)$ gate at $η/2π=0.2$ GHz, in numerical simulations the path-shaping pulse reduces the dephasing exposure by ${\sim}21\%$ relative to cosine DRAG and the independently simulated Lindblad excess leakage by ${\sim}20\%$, consistent with $P_{\mathrm{excess}}^φ\simeqγ_φT\bar{P}_{A}^{\mathrm{deph}}$, whereas matched-budget endpoint-only and spectral-null controls leave it essentially unchanged. The residual endpoint floor splits exactly into a $|2\rangle$ back-action and a $|3\rangle$ cascade, which the two tones cancel one-to-one, driving the floor at the path-exposure knee from ${\sim}7\times10^{-7}$ to ${\sim}3\times10^{-8}$ without perturbing the path. By separating transient exposure from endpoint leakage, PESP turns leakage suppression in fast weakly anharmonic gates into a modular, interpretable control problem: dephasing-induced leakage and the coherent residual error are reduced by separate, individually verifiable modules.

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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
Programmable exchange interactions support quantum gates and many-body simulation in superconducting circuits. Fast excitation transfer, however, opens two leakage pathways in weakly anharmonic transmons, degrading gates and driving simulated dynamics outside the encoded state space. We introduce parametric derivative removal by adiabatic gate (PDRAG) to suppress both pathways while preserving the target exchange. Their conjugate structure determines first- and second-derivative corrections implemented through one real frequency command. At g/2π=100g/2π=100g/2π=100 MHz, calibrated PDRAG achieves a geometric-mean leakage reduction of 5.27×1055.27\times10^55.27×105 relative to the base pulse across 12.5--35 ns in Duffing simulations. At 13 ns, endpoint leakage reaches 1.98×10−71.98\times10^{-7}1.98×10−7 for the calibrated full-exchange pulse. Transferring the derivative coefficients to a charge Hamiltonian gives a mean 893-fold reduction over 12.5--22 ns after amplitude and carrier recalibration. Floquet return interference and charge-induced gap shifts explain the calibration and transfer gains, connecting compact pulse design to leakage-suppressed programmable interactions.
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.
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.
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.