Strongly driven superconducting circuits are a versatile platform to implement a multitude of Hamiltonians for quantum computation, simulation, and sensing. Unfortunately, they can display complex dynamics with instabilities, so predicting and preventing these instabilities is crucial for applications. This paper proposes an inductively shunted transmon qubit as the elementary circuit optimized for strong parametric drives. Developing a numerical approach that avoids the limitations of perturbative analysis, the authors demonstrate that adding the inductive shunt significantly extends the range of pump powers in which the circuit is stable.
Strongly driven superconducting circuits are a versatile platform to implement a multitude of Hamiltonians for quantum computation, simulation, and sensing. Unfortunately, they can display complex dynamics with instabilities, so predicting and preventing these instabilities is crucial for applications. This paper proposes an inductively shunted transmon qubit as the elementary circuit optimized for strong parametric drives. Developing a numerical approach that avoids the limitations of perturbative analysis, the authors demonstrate that adding the inductive shunt significantly extends the range of pump powers in which the circuit is stable.
Strongly driven superconducting Josephson circuits are instrumental in emulating a variety of Hamiltonians that are useful for quantum information processing. However, such a time-dependent, nonlinear, open quantum system can display complex dynamics that lead to degradation of coherence times, instabilities, and chaotic behavior. Here the authors observe an instability that results in the escape of a circuit's mode into states that are not confined by the Josephson cosine potential. This work guides us toward circuit designs that prevent instabilities, and thus are suitable for parametric pumping and quantum information processing.
Strong microwave drives enable fast measurement and parametric control in superconducting circuits but can induce transitions out of the intended low-energy manifold. We develop a unified description of strong-drive limits in flux- and charge-driven Josephson circuits across drive frequency and dc flux bias. Using classical phase-space analysis and Floquet--Markov simulations, we identify distinct low- and high-frequency mechanisms. At low frequency, we characterize bound-state resonances and separatrix chaos and find that the flux-drive chaos threshold depends strongly on dc flux bias. At high frequency, these mechanisms are suppressed, and the dissipative steady state transfers from the central bound-state sector to outer resonances formed by above-barrier running trajectories. The resulting unbound-resonance threshold is nearly independent of drive frequency and circuit parameters over the regime studied and is controlled primarily by dc flux bias. Coherent simulations show that parametric operation persists beyond this threshold, but at a reduced rate, setting an effective upper bound on the achievable operation speed. We derive analytical criteria for both thresholds, validate them numerically, and experimentally confirm the predicted dc-bias dependence of the low-frequency threshold in a flux-driven SQUID. We also determine the timescales for transfer into the unbound-resonance regime and relaxation back to the bound-state manifold after the drive is removed. Finally, we relate the stability limits to a complementary picture based on the junction critical current and extend the framework to multitone drives and inductively shunted circuits. Together, these results identify the mechanisms limiting strong driving and suggest routes to extend the stable operating range of Josephson circuits.
Abstract Inductively shunted transmon qubits(IST) have emerged as one of the most promising candidates for superconducting quantum computing, exhibiting remarkable resilience to both charge and flux noise as a qubit. In this work, we investigate, analytically and numerically, the potential of the IST as a coupler. Compared to the conventional transmon couplers, significant advantages due to the addition of an inductive shunt is revealed, and the unique flux-tunability makes it an ideal candidate for implementing coupling between two transmons. Moreover, a novel coupling circuit is investigated through numerical simulations, demonstrates high-contrast switching of qubit–qubit interactions under the control of an external flux, realizing a two-qubit controlled-Z (CZ) gate with an average fidelity above 99.99%.
Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.
We present a general approach for analyzing arbitrary parametric processes in Josephson circuits within a single-degree-of-freedom approximation. Introducing a systematic normal-ordered expansion for the Hamiltonian of parametrically driven superconducting circuits, we present a flexible procedure to describe parametric processes and to compare and optimize different circuit designs for particular applications. We obtain formally exact amplitudes [“supercoefficients” (SCs)] of these parametric processes for driven circuits based on superconducting nonlinear asymmetric inductive elements and superconducting quantum interference devices. The corresponding amplitudes contain complete information about the circuit topology, the form of the nonlinearity, and the parametric drive, making them, in particular, well suited for the study of the strong-drive regime. We present a closed-form expression for SCs describing circuits without stray inductors and a tractable formulation for those with it. We demonstrate the versatility of the approach by applying it to the estimation of Kerr-cat qubit Hamiltonian parameters and by examining the criterion for the emergence of chaos in Kerr-cat qubits. Additionally, we extend the approach to multiple-degree-of-freedom circuits comprising multiple linear modes weakly coupled to a single nonlinear mode. We apply this generalized framework to study the activation of a beam-splitter interaction between two cavities coupled via driven nonlinear elements. Finally, utilizing the flexibility of the proposed approach, we separately derive SCs for the higher-harmonics model of Josephson junctions, circuits with multiple drives, and the expansion of the Hamiltonian in the exact eigenstate basis for Josephson circuits with specific symmetries.
We experimentally investigate inductively shunted transmon-type artificial atoms as an alternative to address the challenges of low anharmonicity and the need for strong charge dispersion in superconducting quantum systems. We characterize several devices with varying geometries and parameters (Josephson energies and capacitances), and find a good agreement with calculations. Our approach allows us to retain the benefits of transmon qubit engineering and fabrication technology and high coherence, while potentially increasing anharmonicity. The approach offers an alternative platform for the development of scalable multi-qubit systems in quantum computing.