Superconducting circuits are being employed for large-scale quantum devices, and a pertinent challenge is to perform accurate numerical simulations of device parameters. One of themost 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.
The ability to perform rapid, high fidelity readout of a qubit state is an important requirement for quantum algorithms and, in particular, for enabling operations such as mid-circuitmeasurements and measurement-based feedback for error correction schemes on large quantum processors. The growing interest in fluxonium qubits, due to their long coherence times and high anharmonicity, merits further attention to reducing the readout duration and measurement errors. We find that this can be accomplished by exploiting the flux tunability of fluxonium qubits. In this work, we experimentally demonstrate flux-pulse-assisted readout, as proposed in Phys. Rev. Applied 22, 014079 (this https URL), in a setup without a quantum-limited parametric amplifier. Increasing the dispersive shift magnitude by almost 20% through flux pulsing, we achieve an assignment fidelity of 94.3% with an integration time of 280 ns. The readout performance is limited by state initialization, but we find that the limit imposed only by the signal-to-noise ratio corresponds to an assignment fidelity of 99.9% with a 360 ns integration time. We also verify these results through simple semi-classical simulations. These results constitute the fastest reported readout of a fluxonium qubit, with the prospect of further improvement by incorporation of a parametric amplifier in the readout chain to enhance measurement efficiency.
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 shuntinginductor 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 flux-pulse-assisted readout offers 5 times improvement in signal to noise ratio after 200 ns integration time. Moreover, we show that the performance improvement persists in the presence of finite measurement efficiency combined with quasi-static flux noise. We suggest energy parameters for the fluxonium architecture that will allow for the implementation of our proposed flux-pulse-assisted readout scheme.