Superconducting circuits are being used for large-scale quantum devices, and a major challenge is to perform accurate numerical simulations of device parameters. One of the most advanced methods for analyzing superconducting circuit designs is the energy-participation-ratio (EPR) method, which constructs quantum Hamiltonians based on the energy distribution extracted from classical electromagnetic simulations. In the EPR approach, we extract linear terms from finite-element simulations and add nonlinear terms using the energy participation ratio extracted from the classical simulations. However, the EPR method relies on a low-order expansion of nonlinear terms, which is prohibitive for accurately describing highly anharmonic circuits. An example of such a circuit is the fluxonium qubit, which has recently attracted increasing attention due to its high lifetimes and low error rates. In this work, we extend the EPR approach to effectively address highly nonlinear superconducting circuits, and, as a proof of concept, we apply our approach to a fluxonium qubit. Specifically, we design, fabricate, and experimentally measure a fluxonium qubit coupled to a readout resonator. We compare the measured frequencies of both the qubit and the resonator to those extracted from the EPR analysis, and we find an excellent agreement. Furthermore, we compare the dispersive shift as a function of external flux obtained from experiments with our EPR analysis and a simpler lumped-element model. Our findings reveal that the EPR results closely align with the experimental data, providing more accurate estimations compared to the simplified lumped-element simulations.

Two-qubit gates constitute fundamental building blocks in the realization of large-scale quantum devices. Using superconducting circuits, two-qubit gates have been implemented in various ways, with each method aiming to maximize gate fidelity. Another important goal of a new gate scheme is to minimize the complexity of gate calibration. In this work, we demonstrate a high-fidelity two-qubit gate between two fluxonium qubits, enabled by an intermediate capacitively coupled transmon. The coupling strengths between the qubits and the coupler are designed to minimize residual crosstalk while still allowing for fast gate operations. The gate is based on frequency selectively exciting the coupler using a microwave drive to complete a 2π rotation, conditional on the state of the fluxonium qubits. When successful, this drive scheme implements a conditional phase gate. Using analytically derived pulse shapes, we minimize unwanted excitations of the coupler and obtain gate errors of 10−2 for gate times below 60 ns. At longer durations, the gate performance is limited by relaxation of the coupler. Our results show how carefully designed control pulses can speed up frequency-selective entangling gates.

Much attention has focused on the transmon architecture for large-scale superconducting quantum devices; however, the fluxonium qubit has emerged as a possible successor. With a shunting inductor in parallel to a Josephson junction, the fluxonium offers larger anharmonicity and stronger protection against dielectric loss, leading to higher coherence times as compared to conventional transmon qubits. The interplay between the inductive and Josephson energy potentials of the fluxonium qubit leads to a rich dispersive-shift landscape when tuning the external flux. Here, we propose to exploit the features in the dispersive shift to improve qubit readout. Specifically, we report on theoretical simulations showing improved readout times and error rates by performing the readout at a flux-bias point with large dispersive shift. We expand the scheme to include different error channels and show that with an integration time of 155 ns, flux-pulse-assisted readout offers about a 5-times improvement in the signal-to-noise ratio. Moreover, we show that the performance improvement persists in the presence of finite measurement efficiency combined with quasistatic flux noise and also when considering the increased Purcell rate at the flux-pulse-assisted readout point. We suggest a set of reasonable energy parameters for the fluxonium architecture that will allow for the implementation of our proposed flux-pulse-assisted readout scheme.