Transitions in an artificial atom, driven nonadiabatically through an energy-level avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistent-current qubit with a large-amplitude radio-frequency field. By applying a biharmonic wave form generated by a digital source, we demonstrate a mapping between the amplitude and phase of the harmonics produced at the source and those received by the device. This allows us to image the actual wave form at the device. This information is used to engineer a desired time dependence, as confirmed by the detailed comparison with a simulation.
Transitions in an artificial atom, driven nonadiabatically through an energy-level avoided crossing, can be controlled by carefully engineering the driving protocol. We have driven a superconducting persistent-current qubit with a large-amplitude radio-frequency field. By applying a biharmonic wave form generated by a digital source, we demonstrate a mapping between the amplitude and phase of the harmonics produced at the source and those received by the device. This allows us to image the actual wave form at the device. This information is used to engineer a desired time dependence, as confirmed by the detailed comparison with a simulation.
We present experiments on the driven dynamics of a two-level superconducting artificial atom. The driving strength reaches 4.78 GHz, significantly exceeding the transition frequency of 2.288 GHz. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. In addition, we observe the role of pulse shaping in the dynamics, as determined by nonadiabatic transitions between Floquet states, and we implement subnanosecond single-qubit operations. These results pave the way to quantum control using strong driving with applications in quantum technologies.
The device for the Josephson flux qubit can be considered as a solid-state artificial atom with multiple energy levels. When a large-amplitude harmonic excitation is applied to the system, transitions at the energy levels avoided crossings produce visible changes in the qubit population over many driven periods that are accompanied by a rich pattern of interference phenomena. We present a Floquet treatment of the periodically time-dependent Schr\"odinger equation of the strongly driven qubit beyond the standard two-level approach. For low amplitudes, the average probability of a given sign of the persistent current qubit exhibits, as a function of the static flux detuning and the driving amplitude, Landau-Zener-St\"uckelberg (LZS) interference patterns that evolve into complex diamondlike patterns for large amplitudes. In the case of highly coherent flux qubits we show that the higher-order diamonds can not be simply described relying on LZS transitions in each avoided crossing considered separately. In addition we propose a spectroscopic method based on starting the system in the first excited state instead of in the ground state, which can give further information on the energy-level spectrum and dynamics in the case of highly coherent flux qubits. We compare our numerical results with recent experiments that perform amplitude spectroscopy to probe the energy spectrum of the artificial atom.
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.
We investigate the amplitude and phase effects of qubit dynamics and excited-state population under the influence of a biharmonic control field. It is demonstrated that the biharmonic driving field can have a significant effect on the behavior of quasienergy level crossing as well as on multiphoton transitions. Also, the interference pattern for the populations of qubit excited states is sensitive to the signal parameters. We discuss the possibility of using these effects for manipulating qubit states and calibrating nanosecond pulses.
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.