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arXiv:2509.23467

Ultrafast Single-Qubit Gates in the Diabatic Regime

Deniz Türkpençe, Selçuk Çakmak

Published Sep 27, 2025• 0 citations
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Abstract

Logic gates in superconducting quantum processors are implemented through precise quantum control techniques in the microwave regime. The choice of drive frequency and other control parameters directly determines the duration of quantum gate operations. Because current devices remain too noisy to reach fault tolerance, reducing gate durations, and thereby the overall circuit depth, is of critical importance. In this work, we present a model of single qubit gate execution in both the adiabatic regime, where the rotating wave approximation (RWA) is valid, and the diabatic regime, where the RWA no longer applies. Using parameters representative of superconducting qubits, we investigate how gates can be driven at durations well below conventional timescales, and we examine the associated limitations, performance trade offs. The results demonstrate that ultrashort control pulses in the diabatic regime can achieve fidelities comparable to those obtained under standard RWA conditions, offering a possible route to faster quantum logic without sacrificing accuracy under idealized conditions.

DOI
10.48550/arxiv.2509.23467

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Logic gates in superconducting quantum processors are implemented through precise quantum control techniques in the microwave regime. The choice of drive frequency and other control parameters directly determines the duration of quantum gate operations. Because current devices remain too noisy to reach fault tolerance, reducing gate durations, and thereby the overall circuit depth, is of critical importance. In this work, we present a model of single qubit gate execution in both the adiabatic regime, where the rotating wave approximation (RWA) is valid, and the diabatic regime, where the RWA no longer applies. Using parameters representative of superconducting qubits, we investigate how gates can be driven at durations well below conventional timescales, and we examine the associated limitations, performance trade offs. The results demonstrate that ultrashort control pulses in the diabatic regime can achieve fidelities comparable to those obtained under standard RWA conditions, offering a possible route to faster quantum logic without sacrificing accuracy under idealized conditions.
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.
Fault-tolerant quantum computing requires high-fidelity quantum gates that are resilient to control errors and device imperfections. Here, we develop energy-optimal control pulses for single-qubit gates that are simultaneously robust against frequency detuning and waveform inhomogeneities while also suppressing leakage outside the computational subspace. Combining the optimized pulse envelopes with an adaptive control scheme, we experimentally demonstrate optimal robust gates on a superconducting quantum processor. For a gate duration of 90ns, we achieve fidelities above 99.9% for the X gate and 99.6% for Hadamard-type gates. For the X gate, we maintain fidelities above 99.5% for simultaneous drive-amplitude variations up to 20% and qubit detuning up to 4 MHz. This robustness outperforms that of conventional Gaussian pulses by an order of magnitude, without much difference in peak gate fidelity. These results establish a route towards robust single-qubit control in large-scale quantum processors, advancing the development of fault-tolerant quantum computing.
We discuss the realization of a universal set of ultrafast single- and two-qubit operations with superconducting quantum circuits and investigate the most relevant physical and technical limitations that arise when pushing for faster and faster gates. With the help of numerical optimization techniques, we establish a fundamental bound on the minimal gate time, which is determined independently of the qubit design solely by its nonlinearity. In addition, important practical restrictions arise from the finite qubit transition frequency and the limited bandwidth of the control pulses. We show that, for highly anharmonic flux qubits and commercially available control electronics, elementary single- and two-qubit operations can be implemented in about 100 ps with residual gate errors below ${10}^{\ensuremath{-}4}$. Under the same conditions, we simulate the complete execution of a compressed version of Shor's algorithm for factoring the number 15 in about 1 ns. These results demonstrate that, compared to state-of-the-art implementations with transmon qubits, a hundredfold increase in the speed of gate operations with superconducting circuits is still feasible.
In many quantum platforms, single-qubit gates are applied using a linear drive resonant with the qubit transition frequency, which is often theoretically described within the rotating-wave approximation (RWA). However, for fast gates on low-frequency qubits, the RWA may not hold and we need to consider the contribution from counterrotating terms to the qubit dynamics. The inclusion of counterrotating terms into the theoretical description gives rise to two challenges. First, it becomes challenging to analytically calculate the time evolution as the Hamiltonian is no longer self-commuting. Moreover, the time evolution now depends on the carrier phase such that, in general, every operation in a sequence of gates is different. In this work, we derive and verify a correction to the drive pulses that minimizes the effect of these counterrotating terms in a two-level system. We then derive a second correction term that arises from noncomputational levels for a strongly anharmonic system. We experimentally implement these correction terms on a fluxonium superconducting qubit, which is an example of a strongly anharmonic, low-frequency qubit for which the RWA may not hold, and demonstrate how fast, high-fidelity single-qubit gates can be achieved without the need for additional hardware and calibration complexities.
We present a theoretical study of single-qubit operations by oscillatory fields on various semiconductor platforms. We explicitly show how to perform faster gate operations by going beyond the universally used rotating-wave approximation (RWA) regime, while using only two sinusoidal pulses. We first show for specific published experiments how much error is currently incurred by implementing pulses designed using standard RWA. We then show that an even modest increase in gate speed would cause problems in using RWA for gate design in the singlet-triplet (ST) and resonant-exchange (RX) qubits. We discuss the extent to which analytically keeping higher orders in the perturbation theory would address the problem. More strikingly, we give a new prescription for gating with strong coupling far beyond the RWA regime. We perform numerical calculations for the phases and the durations of two consecutive pulses to realize the key Hadamard and $\frac{\ensuremath{\pi}}{8}$ gates with coupling strengths up to several times the qubit splitting. Working in this manifestly non-RWA regime, the gate operation speeds up by two to three orders of magnitude and nears the quantum speed limit without requiring complicated pulse shaping or optimal control sequences.
Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing.Unfortunately, analytically constructing shortcuts to adiabaticity for systems having complex interactions and more than a few levels is a challenging task.This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made].Here we develop an analytic approach that allows one to go beyond these limitations.Our method is general and results in analytically derived pulse shapes that correct both nonadiabatic errors and non-RWA errors.We also show that our approach can yield pulses requiring a smaller driving power than conventional nonadiabatic protocols.We show in detail how our ideas can be used to analytically design high-fidelity single-qubit "tripod" gates in a realistic superconducting fluxonium qubit.