Precise quantum control relies on a deep understanding of the dynamics of quantum systems under external drives. This study investigates the impact of anharmonicity on qubit dynamics under conditions typical for two-qubit entangling gates activated by weak near-resonant microwave drives. We measure the Rabi oscillation frequency as a function of drive amplitude and detuning. Our results reveal a linear dependence of the squared Rabi frequency on the squared drive amplitude, which relates to the ratio of detuning to anharmonicity, demonstrating strong agreement between experimental data and analytical predictions. Additionally, we analyze the leakage and phase errors arising from inaccurate Rabi frequency adjustments in the CZ gate implementation on fluxonium qubits driven by a microwave signal applied to the coupler [Simakov et al., PRX Quantum 4, 040321 (2023)].
Precise quantum control relies on a deep understanding of the dynamics of quantum systems under external drives. This study investigates the impact of anharmonicity on qubit dynamics under conditions typical for two-qubit entangling gates activated by weak near-resonant microwave drives. We measure the Rabi oscillation frequency as a function of drive amplitude and detuning. Our results reveal a linear dependence of the squared Rabi frequency on the squared drive amplitude, which relates to the ratio of detuning to anharmonicity, demonstrating strong agreement between experimental data and analytical predictions. Additionally, we analyze the leakage and phase errors arising from inaccurate Rabi frequency adjustments in the CZ gate implementation on fluxonium qubits driven by a microwave signal applied to the coupler [Simakov et al., PRX Quantum 4, 040321 (2023)].
We propose a family of microwave-activated entangling gates on two capacitively coupled fluxonium qubits.A microwave pulse applied to either qubit at a frequency near the half-frequency of the |00 -|11 transition induces two-photon Rabi oscillations with a negligible leakage outside the computational subspace, owing to the strong anharmonicity of fluxoniums.By adjusting the drive frequency, amplitude, and duration, we obtain the gate family that is locally equivalent to the fermionic-simulation gates such as √ SWAP-like and controlled-phase gates.The gate error can be tuned below 10 -4 for a pulse duration under 100 ns without excessive circuit parameter matching.Given that the fluxonium coherence time can exceed 1 ms, our gate scheme is promising for large-scale quantum processors.
The resonator-induced phase gate is a two-qubit operation in which driving a bus resonator induces a state-dependent phase shift on the qubits equivalent to an effective ZZ interaction. In principle, the dispersive nature of the gate offers flexibility for qubit parameters. However, the drive can cause resonator and qubit leakage, the physics of which cannot be fully captured using either the existing Jaynes-Cummings or Kerr models. In this paper, we adopt an ab initio model based on Josephson nonlinearity for transmon qubits. The ab initio analysis agrees well with the Kerr model in terms of capturing the effective ZZ interaction in the weak-drive dispersive regime. In addition, however, it reveals numerous leakage transitions involving high-excitation qubit states. We analyze the physics behind such novel leakage channels, demonstrate the connection with specific qubit-resonator frequency collisions, and lay out a plan toward device parameter optimization. We show that this type of leakage can be substantially suppressed using very weakly anharmonic transmons. In particular, weaker qubit anharmonicity mitigates both collision density and leakage amplitude, while larger qubit frequency moves the collisions to occur only at large anharmonicity not relevant to experiment. Our work is broadly applicable to the physics of weakly anharmonic transmon qubits coupled to linear resonators. In particular, our analysis confirms and generalizes the measurement-induced state transitions noted in Sank et al. [Phys. Rev. Lett. 117, 190503 (2016)] and lays the groundwork for both strong-drive resonator-induced phase gate implementation and strong-drive dispersive qubit measurement.
Rabi oscillations describe the coherent evolution of a two-level quantum system under the influence of a resonant driving field. They are central to quantum computing and determine the utility of qubits. Reliable control of these oscillations requires precise calibration of the driving field; however, experimental implementations are subject to imperfections that stray from what is ideal. One source of error is amplitude miscalibration, where the strength of the applied control pulse fluctuates around its intended value.In this study, the effects of amplitude error on Rabi oscillations were investigated using a formulaic simulation of a single-qubit system. The system was modeled using the Cirq quantum circuit framework, where Rabi oscillations were represented as rotations on the Bloch sphere. Amplitude divergence was incorporated by modifying the Rabi drive strength with Gaussian-distributed noise. The resulting state evolution was compared with the ideal theoretical oscillation in order to visualize the impact of stochastic amplitude variations on qubit dynamics.This model provides a simplified framework for examining how imperfect calibration influences coherent quantum state evolution in two-level systems.
Achieving fast gates and high-fidelity readout in superconducting quantum circuits often benefits from the use of large amplitude microwave drives. As the strength increases, unwanted effects such as excitation out of the logical states also become more prevalent. In transmon qubits, coherent controls relying on sub-resonant drives are fundamentally limited by the eventual appearance of strong hybridization in the spectrum. Understanding how this threshold depends on intrinsic device parameters is vital for the design and operation of circuits utilizing the transmon as a source of nonlinearity. In this work, we present an experimental study of 14 transmons with a wide range of anharmonicities, and use comparison with Floquet branch analysis and semiclassical simulations to establish a straightforward relationship between the critical value of the effective drive amplitude ηmax and the ratio γ=ωq/α, where ωq is the transmon frequency and −α is the anharmonicity. For the case where the transmon is used as a parametrically driven coupler, these results further allow us to estimate maximum parametric interaction rates, which informs the circuit design process for optimizing gate rates and fidelities.
Coherent control of two-level quantum systems is typically achieved using resonant driving fields, forming the basis for qubit operations. Here, we report a mechanism for inducing complete Rabi oscillations in monochromatically driven two-level quantum systems, when the drive frequency is much larger than the Larmor frequency of the qubit. This effect$\unicode{x2015}$Rabi oscillations induced by nonresonant gyrating drive (RING)$\unicode{x2015}$requires a gyrating control field, i.e., an elliptic drive trajectory that encloses a nonzero area per cycle. We illustrate the effect with numerical simulations, and provide an analytical understanding via a simple effective Hamiltonian obtained from Floquet theory and perturbation theory. We show that RING enables coherent oscillations without relying on resonant energy exchange, allows for high-pass noise filtering, provides access to non-Abelian phases in finite magnetic fields. We detail a realization in electrically driven spin-orbit qubits and argue that the RING mechanism enables amplification of the Rabi frequency using the same gate voltage amplitudes at higher drive frequencies. Our results broaden the landscape of quantum control techniques, by highlighting a pathway to achieving coherent oscillations under off-resonant driving 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.