Upper speed limit on parametric gates in Josephson junction-based circuits (part I)

In superconducting quantum systems, parametric driving can realize versatile and high-fidelity quantum control by activating nonlinear Hamiltonian terms with strong off-resonant driving. However, multiple factors can limit the fidelity of the parametric gates. In experiments, it is observed that the quantum coupler and coupled qubits rapidly leak to high excited states when the drive strength exceeds a threshold, limiting the maximum gate speed. To understand this limitation, we experimentally investigate it using a transmon qubit as a prototypical nonlinear element. The sudden onset of transitions to high transmon excited states is observed at a critical drive amplitude, which can be understood by the emergence of chaotic behavior of the driven nonlinear system. We also provide theoretical predictions and an explanation of this limitation, detailed in the second part of this talk, showing excellent agreement with experiment data. This theory can be further extended to more complicated systems to help improve the speed of multi-qubit parametric gates.