It is well known that superconducting waveguides strongly attenuate the propagation of electromagnetic waves with frequencies beyond the superconducting gap. In circuit QED, the interactionbetween non-linear charge qubits and superconducting resonators invariably involves the qubit coupling to a large set of resonator modes. So far, strong dispersion effects near and beyond the superconducting-gap have been ignored in quantization models. Rather, it is assumed that the superconducting resonator behaves ideally across the large frequency intervals. We present a quantization approach which includes the superconducting frequency-dependent surface impedance and demonstrate that superconducting dispersion plays a role in determining the effective light-matter interaction cut-off.
The measurement of a superconducting qubit is implemented by coupling it to a resonator. The common choice is transverse coupling, which, in the dispersive approximation, introducesan interaction term which enables the measurement. This cross-Kerr term provides a qubit-state dependent dispersive shift in the resonator frequency with the device parameters chosen carefully to get sufficient signal while minimizing Purcell decay of the qubit. We introduce a two-mode circuit, nicknamed quantromon, with two orthogonal modes implementing a qubit and a resonator. Unlike before, where the coupling term emerges as a perturbative expansion, the quantromon has intrinsic cross-Kerr coupling by design. Our experiments implemented in a hybrid 2D-3D cQED architecture demonstrate some unique features of the quantromon like weak dependence of the dispersive shift on the qubit-resonator detuning and intrinsic Purcell protection. In a tunable qubit-frequency device, we show that the dispersive shift (2χ/2π) changes by only 0.8 MHz while the qubit-resonator detuning (Δ/2π) is varied between 0.398 GHz – 3.288 GHz. We also demonstrate Purcell protection in a second device where we tune the orthogonality between the two modes. Finally, we demonstrate a single-shot readout fidelity of 98.3% without using a parametric amplifier which is comparable to the state-of-the-art and suggests a potential simplification of the measurement circuitry for scaling up quantum processors.
Implementing a precise measurement of the quantum state of a qubit is very critical for building a practical quantum processor as it plays an important role in state initializationand quantum error correction. While the transmon qubit has been the most commonly used design in small to medium-scale processors, the fluxonium qubit is emerging as a strong alternative with the potential for high-fidelity gate operation as a result of the high anharmonicity and high coherence achievable due to its unique design. Here, we explore the measurement characteristics of a tantalum-based high-coherence fluxonium qubit and demonstrate single-shot measurement fidelity (assignment fidelity) of 96.2% and 97.8% without and with the use of a Josephson Parametric Amplifier respectively. We study the back-action of the measurement photons on the qubit and measure a QND (repeatability) fidelity of 99.6%. We find that the measurement fidelity and QND nature are limited by state-mixing errors and our results suggest that a careful study of measurement-induced transitions in the fluxonium is needed to further optimize the readout performance.