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.
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.
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 RX(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⟩ and ∣3⟩ channels, lowering the coherent endpoint leakage from approximately 7×10−7 to 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.
Logic gates in superconducting quantum processors are implemented through precisely shaped microwave pulses, whose durations are constrained by both device coherence and the multilevel structure of artificial atoms. While single-qubit fidelities above 0.999 are routinely achieved, the physical execution time of these gates remains a major bottleneck for deep quantum circuits. Here we examine single-qubit control across adiabatic [where the rotating-wave approximation (RWA) is valid], intermediate, and diabatic driving regimes using both an ideal two-level model and a realistic weakly anharmonic transmon Hamiltonian. By sweeping pulse durations and drive strengths over experimentally relevant ranges, we compare performance trade-offs and identify the conditions under which ultrashort gates remain viable. Our simulations uncover a quantitative speed-limit mechanism intrinsic to weakly anharmonic superconducting qubits: leakage to higher levels rises sharply once the peak Rabi rate exceeds a fixed fraction of the anharmonicity. Across all pulse shapes and driving regimes studied, we find a consistent numerical threshold at Ω max /|Δ|≈0.15−0.20, where Ω max denotes the peak drive (Rabi) amplitude and Δ is the transmon anharmonicity. Beyond this ratio, gate fidelity deteriorates regardless of waveform engineering. This boundary, obtained from full multilevel time-domain simulations spanning adiabatic, intermediate, and diabatic regimes, constitutes a previously unreported characterization of the fundamental leakage barrier in transmon devices. Our results, therefore, provide the first unified quantitative map linking pulse duration, driving strength, and anharmonicity, establishing why realistic superconducting qubits cannot sustain picosecond-scale gates despite ideal two-level predictions, and offering a practical benchmark for next-generation architectures seeking shorter, high-fidelity control.
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=100 MHz, calibrated PDRAG achieves a geometric-mean leakage reduction of 5.27×105 relative to the base pulse across 12.5--35 ns in Duffing simulations. At 13 ns, endpoint leakage reaches 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.
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
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.
We report phase-resolved measurements of amplitude-phase coupling (APC) in strongly driven superconducting transmon qubits, a symmetry-based mechanism analysis, and follow-up experiments on a second device. On a Rigetti Ankaa-3 transmon (1000 shots per point, five drive amplitudes, matched root-mean-square drive), the fitted optimal control phase ϕ∗(A) drifts by more than 3 rad across the explored amplitude range for both a rectangular reference pulse and a self-intersecting Figure-8 trajectory, and the phase contrast of the two waveform families exhibits a reproducible low-/high-amplitude crossover. Theoretically, we prove that in the resonant rotating frame of the three-level Duffing model a constant-phase rectangular drive cannot produce any phase-dependent population response: CRect=0 exactly. Any measured rectangular phase contrast is therefore a probe of physics outside this model (beyond-rotating-wave carrier-phase dependence, control-chain distortion, readout imperfections). The Figure-8 waveform breaks the symmetry intrinsically through its 2:1 Fourier content; a third-order resonance ω+ω−2ω=0 mediated by the anharmonic level ∣2⟩ predicts CF8∝A6N2 at weak drive, confirmed by direct numerical propagation (fitted log-log slope 5.97±0.02; loop-number ratio 2434 vs. predicted 2500). On the successor device Cepheus-1-108Q, the predicted phase contrast lies below the binomial shot-noise floor at the accessible amplitudes, but the same dataset reveals a stronger signature of the underlying first-order average-Hamiltonian cancellation: the phase-averaged survival probability of the Figure-8 train remains pinned at ⟨P(∣0⟩)⟩ϕ≈0.985 across all tested conditions, while the isenergetic rectangular reference sweeps the full range 0.24-0.93—an approximately 70-fold suppression of the Rabi-drive response. Together these results identify APC as a measurable control-landscape feature with distinct intrinsic and extrinsic components, and demonstrate a calibration-free, amplitude-insensitive idling property of Figure-8 pulse trains.