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.
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.
In circuit quantum electrodynamical systems, the quasiparticle-related losses in Josephson junctions are suppressed due to the gap in the superconducting density of states which is much higher than the typical energy of a microwave photon. In this work, we show that a strong drive even at a frequency lower than twice the superconductor gap parameter can activate dissipation in the junctions due to photon-assisted breaking of the Cooper pairs. Both the decay rate and noise strength associated with the losses are sensitive to the dc phase bias of the junction and can be tuned in a broad range by the amplitude and the frequency of the external driving field, making the suggested mechanism potentially attractive for designing tunable dissipative elements. We also predict pronounced memory effects in the driven Josephson junctions, which are appealing for both theoretical and experimental studies of non-Markovian physics in superconducting quantum circuits. We illustrate our theoretical findings by studying the spectral properties and the steady-state population of a low-impedance resonator coupled to the driven Josephson junction: we show the emergence of non-Lorentzian spectral lines and broad tunability of effective temperature of the steady state.
This thesis discusses a series of experimental and theoretical studies on fast control and decoherence in superconducting quantum circuits. These two subjects are complementary aspects of the problem of improving the gate fidelities in quantum information processing devices based on superconducting circuits. \n \nIn the first part of this thesis, we present experiments on fast control of a superconducting flux qubit using strong driving. We explore driving with short pulses and a driving strength significantly exceeding the transition frequency. The observed dynamics is described in terms of quasienergies and quasienergy states, in agreement with Floquet theory. We observe the role of pulse shaping in the dynamics, as determined by non-adiabatic transitions between Floquet states. In addition, based on adiabatic perturbation theory in the Floquet picture, we propose a control scheme for fast and high-fidelity single-qubit operations with strong driving. These results pave the way to quantum control with a fidelity beyond the threshold of fault-tolerant quantum computation. \n \nIn the second part of this thesis, we discuss experimental methods and present the characterization of decoherence in superconducting resonators and superconducting qubits. Firstly, we present an analysis method on the measurements of photon loss in superconducting resonators. We use this method to characterize the microwave loss of aluminum oxide, an important material in superconducting circuits. The power and temperature dependence of the measured loss is consistent with loss due to two-level defects in amorphous materials. Secondly, we present experimental results on decoherence and noise spectroscopy of a superconducting flux qubit. Using the qubit as a noise spectrometer, we perform detailed measurements on the power spectral density of the flux noise in superconducting circuits over a wide range of frequencies, from 10^-3 to 10^8 Hz, and over a temperature range from 35 to 130 mK. We also present measurements of frequency and temperature dependence of the qubit energy relaxation.
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.
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.
Superconducting quantum circuits rely on strong drives to implement fast gates, high-fidelity readout, and state stabilization. However, these drives can induce uncontrolled excitations, so-called "ionization", that compromise the fidelity of these operations. While now well-characterized in the context of qubit readout, it remains unclear how general this limitation is across the more general setting of parametric control. Here, we demonstrate that a nonlinear coupler, exemplified by a transmon, undergoes ionization under strong parametric driving, leading to a breakdown of coherent control and thereby limiting the accessible gate speeds. Through experiments and numerical simulations, we associate this behavior with the emergence of drive-induced chaotic dynamics, which we characterize quantitatively using the instantaneous Floquet spectrum. Our results reveal that the Floquet spectrum provides a unifying framework for understanding strong-drive limitations across a wide range of operations on superconducting quantum circuits. This insight establishes fundamental constraints on parametric control and offers design principles for mitigating drive-induced decoherence in next-generation quantum processors.
The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature Tcr, in the presence of strong resonant ac driving have been investigated. The SQUID contains two Nb/Al-AlOx/Nb tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power W and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current I and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As W further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower I. At certain W, a second resonant peak appears, which can locate at very low I depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at T⪡Tcr, escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.