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arXiv:2506.03456

Exceeding the Parametric Drive Strength Threshold in Nonlinear Circuits

Mingkang Xia, Cristóbal Lledó, Matthew Capocci, Jacob Repicky, Benjamin D’Anjou, Ian Mondragon-Shem, Kaufman, Ryan, Jens Koch, Alexandre Blais, Michael Hatridge

Published Jun 3, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2506.03456

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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.
Transmon qubits are ubiquitously used in superconducting quantum information processor architectures.Strong drives are required to realize fast, high-fidelity, gates and measurements, including parametrically activated processes.Here, we show that even off-resonant drives, in regimes routinely used in experiments, can cause strong modifications to the structure of the transmon spectrum rendering a large part of it chaotic.Accounting for the full nonlinear dynamics of the transmon in a Floquet-Markov formalism, we find that these chaotic states, often neglected through the hypothesis that the anharmonicity is weak, strongly impact the lifetime of the transmon's computational states.In particular, we observe that chaos-assisted quantum phase slips greatly enhance band dispersions.In the presence of a measurement resonator, we find that approaching chaotic behavior correlates with strong transmon-resonator hybridization, and an average resonator response centered on the bare resonator frequency.These results lead to a photon-number threshold characterizing the appearance of chaos-induced quantum demolition effects during strong-drive operations, such as dispersive qubit readout.The phenomena described here are expected to be present in all circuits based on low-impedance Josephson junctions.
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⁡η_{\max}ηmax​ and the ratio γ=ωq/αγ=ω_q/αγ=ωq​/α, where ωqω_qωq​ is the transmon frequency and −α-α−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.
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.
Microwave drives are essential for implementing control and readout operations in superconducting quantum circuits. However, increasing the drive strength eventually leads to unwanted state transitions which limit the speed and fidelity of such operations. In this work, we systematically investigate such transitions in a fixed-frequency qubit subjected to microwave drives spanning a 9-GHz frequency range. We identify the physical origins of these transitions and classify them into three categories: (1) resonant energy exchange with parasitic two-level systems (TLSs), activated by drive-induced ac-Stark shifts, (2) multiphoton transitions to noncomputational states, intrinsic to the circuit Hamiltonian, and (3) inelastic scattering processes in which the drive causes a state transition in the superconducting circuit, while transferring excess energy to a spurious electromagnetic mode or TLS material defect. We show that the Floquet steady-state simulation, complemented by an electromagnetic simulation of the physical device, accurately predicts the observed transitions that do not involve TLS. Our results provide a comprehensive classification of these transitions and offer mitigation strategies through informed choices of drive frequency as well as improved circuit design.
Superconducting circuits are a leading platform for scalable quantum computing, where parametric modulation is a widely used technique for implementing high-fidelity multi-qubit operations. A critical challenge, however, is that this modulation can induce a dense landscape of parasitic couplings, leading to detrimental frequency collisions that constrain processor performance. In this work, we develop a comprehensive numerical framework, grounded in Floquet theory, to systematically analyze and mitigate these collisions. Our approach integrates this numerical analysis with newly derived analytical models for both qubit-modulated and coupler-modulated schemes, allowing us to characterize the complete map of parasitic sideband interactions and their distinct error budgets. This analysis forms the basis of a constraint-based optimization methodology designed to identify parameter configurations that satisfy the derived physical constraints, thereby avoiding detrimental parasitic interactions. We illustrate the utility of this framework with applications to analog quantum simulation and gate design. Our work provides a predictive tool for co-engineering device parameters and control protocols, enabling the systematic suppression of crosstalk and paving the way for large-scale, high-performance quantum processors.
The ability to perform fast, high-fidelity entangling gates is a requirement for a viable quantum processor. In practice, achieving fast gates often comes with the penalty of strong-drive effects that are not captured by the rotating-wave approximation. These effects can be analyzed in simulations of the gate protocol, but those are computationally costly and often hide the physics at play. Here, we show how to efficiently extract gate parameters by directly solving a Floquet eigenproblem using exact numerics and a perturbative analytical approach. As an example application of this toolkit, we study the space of parametric gates generated between two fixed-frequency transmon qubits connected by a parametrically driven coupler. Our analytical treatment, based on time-dependent Schrieffer-Wolff perturbation theory, yields closed-form expressions for gate frequencies and spurious interactions, and is valid for strong drives. From these calculations, we identify optimal regimes of operation for different types of gates including iiiswap, controlled-Z, and cnot. These analytical results are supplemented by numerical Floquet computations from which we directly extract drive-dependent gate parameters. This approach has a considerable computational advantage over full simulations of time evolutions. More generally, our combined analytical and numerical strategy allows us to characterize two-qubit gates involving parametrically driven interactions, and can be applied to gate optimization and cross-talk mitigation such as the cancelation of unwanted ZZZZZZ interactions in multiqubit architectures.