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=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.
High-fidelity control of superconducting qubits requires carefully shaped microwave pulses to avoid several different kinds of error at once. This article is a pedagogical bridging text aimed at upper-level undergraduate and early graduate students who have completed an introductory quantum mechanics course and a first course in quantum computing or quantum information, but who have not yet encountered the physical implementation of qubit gates. We integrate physical intuition for pulse design, analytical gate-level descriptions, and practical hardware considerations into a single, derivation-driven narrative, with explicit learning objectives. We begin with simple pulse envelopes and their spectral properties, showing how finite bandwidth produces leakage outside the computational subspace. This motivates the derivative removal by adiabatic gate (DRAG) technique, which we derive explicitly using the Magnus expansion, obtaining a clear, order-by-order account of which physical error channel appears at which order and why DRAG's cancellation is necessarily incomplete. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Finally, we extend the discussion to two-qubit operation via the cross-resonance gate, and interpret how driving the control qubit at the target qubit's transition frequency necessarily produces several unwanted interaction terms alongside the desired one, and how successive generations of pulse-engineering strategies have been designed to suppress them.
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
2.0×10−5, and obtain fidelities above
99.98% for pulse durations down to 6.8 ns for both
X and
X/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
10−6. The presented approach can be readily applied to other qubit types as well.
A fundamental challenge in quantum computing is to increase the number of operations within the qubit coherence time. While this can be achieved by decreasing the gate duration, the use of shorter signals increases their bandwidth and can cause leakage into energetically separated states. A common method to suppress leakage for short pulses is the Derivative Removal by Adiabatic Gate (DRAG) method, which, however, relies on IQ modulation of radio-frequency (RF) signals, thus cannot be applied to the baseband signals, e.g., for semiconductor spin qubits. This paper proposes a novel technique, Delayed Leakage Reduction (DLR), that suppresses leakage at targeted frequencies even for baseband control by using time-delayed repetitions of the control signal to enable rapid, high-fidelity operations. We apply DLR on the adiabatic CZ gate between two spin qubits and achieve fidelities exceeding 99.9% within 9.4 ns for a resonance frequency difference of only 100 MHz. Towards the experimental realization of the proposed control method, we also assess the impact on the fidelity of the sampling rate, noise, and signal quantization of the electronic hardware generating the control pulse, thus setting the minimum hardware requirements for any experimental demonstration.
Recent achievements in the physical size of quantum computers based on superconducting qubits foresee reaching the next milestones of the exponentially growing number of qubits. The promises in the scalability present opportunities in integrated control electronics operating at 4K stage in the dilution refrigerator. In addition to the number of physical qubits, however, commercialization necessitates a further increase in the number of consecutive high-fidelity gate operations within a coherence time of
∼100μs. It leads to the stringent requirement on the duration of qubit-driving microwave pulse
(i.e., <20ns). The microwave pulses should only drive
∣0⟩↔∣1⟩for single qubit gate operations while avoiding leakage to
∣1⟩↔∣2⟩which is the major factor that degrades the gate fidelity. The frequency for
∣1⟩↔∣2⟩,ω12, is typically lower than the frequency for
∣0⟩↔∣1⟩,ω01, by
2π×(160MHz−to−360MHz). The frequency difference
(ω01−ω12), called anharmonicity, is an individual qubit characteristic and becomes the margin for spectral management. But, a short driving pulse even with Gaussian, sine, or raised-cosine shapes eventually widens the spectral width. It would range a few hundred MHz and result in a considerable spectral leakage at
ω12. To mitigate this spectral leakage, the derivative removal by adiabatic gate (DRAG) has been adopted in the pulse shaping [1], [2]. As shown in Fig. 34.4.1, the first-order DRAG pulse shaping is realized by adding two parts as \begin{equation*}\mathsf{O}(\mathrm{t})=\mathsf{S}_{\mathsf{M}}(\mathsf{t})\cdot\mathsf{cos}(\omega_{01}\mathsf{t}+\varphi)+\mathsf{q}_{\mathsf{scale}}\mathsf{S}_{\mathsf{M}}(\mathsf{t})^{\prime}\cdot\mathsf{sin}(\omega_{01}\mathsf{t}+\varphi)\end{equation*} where
SM(t)is the main pulse shape and
qscaleis a coefficient inversely proportional to the anharmonicity. This first-order DRAG makes an asymmetrical spectrum that lowers the left frequency side and raises the right frequency side. Since the
ω12is always on the left side of
ω01, the DRAG can effectively minimize the leakage.