Measurement-Induced State transitions in Inductively-Shunted Transmons

Abstract

Fast and high-fidelity qubit measurement plays a key role in quantum error correction. In superconducting qubits, measurement is typically performed using a resonant microwave drive on a readout resonator dispersively coupled to the qubit. Shorter measurement times require larger numbers of photons populating the readout resonator, which ultimately leads to undesired measurementinduced state transitions (MIST) of the qubit. MIST can be particularly problematic because these transitions often leave the qubit in a high energy state, and the MIST locations in readout parameter space drift as a function of qubit offset charge. In transmon qubits, these drifts have been avoided using very large qubit-resonator detunings or dedicated offset charge biases. In this work, we take an alternative approach and add an inductive shunt to the transmon to eliminate the offset charge dependence and stabilize the MIST. We experimentally characterize MIST in several different inductively-shunted transmons, in agreement with quantum and semiclassical models for MIST. These results extend to other inductively-shunted qubits.

Figures (7)

• Figure 1: Illustration of the device. (a) Circuit diagram of the qubit-resonator system without readout multiplexing. Each qubit has a separate capacitive drive and flux bias (blue). The readout resonator is coupled to a shared Purcell filter (pink). (b) The circuit schematic for a readout line. The qubit (green) and ground plane (gray) patterns are shown with equivalent circuit diagrams replacing the patterns for the couplers and readout circuit. Note the large capacitor pads of the IST, which ease connectivity in devices with large qubit numbers.
• Figure 2: The spectrum of the qubit-resonator system vs. external bias for Q1 (a) and Q2 (b). Experimentally measured values are shown as circles. Fits to \ref{['eq:full_circuit_model']} are shown as lines and the resulting full-circuit parameters are given in \ref{['tab:parameters']}. Divergences near avoided level crossings are excluded from the plot for clarity. The black dotted lines show the qubit transitions as modeled by \ref{['eq:freq_and_eta']}, including second-order shifts due to the coupling to the resonator. The analytic expressions are in excellent agreement with the data for the majority of fluxes. Deviations are observed around the qubit-resonator avoided level crossings, as expected from second-order perturbation theory, and near the lower flux insensitive point for Q1, where the IST potential approaches the onset of a double-well structure where the Kerr approximation fails.
• Figure 3: Ground state MIST experimental data and comparison to models. Data and parameters are presented for two different designs of IST qubits Q1 (a) and Q2 (b). MIST behavior is significantly different when the qubit is above the readout resonator in frequency (a) or below it in frequency (b).
• Figure 4: Leakage data for both IST and Transmon qubits vs. applied resonator photon number. The data was taken continuously over the course of 24 hours. The median of these datasets is shown as a solid color while the semi-transparent lines show individual runs. There is a qualitative difference in variability between the transmon and IST qubit types as expected from the lack of offset charge in IST qubits.
• Figure 5: Coherence data for IST qubits Q1 (a, b) and Q2 (c, d). Panels (a) and (c) show the population versus time at different qubit frequencies. Pannels (b) and (d) report the fitted exponential decay time associated with each frequency. The dark curves are the data for Q1 and Q2. Other qubits on the chip are plotted for comparison in the lighter color. Note that at some of the $T_1$ minima, the population oscillates over time, making this fit value not meaningful. The dashed lines show the expected $T_1$ using the measured qubit parameters in \ref{['tab:parameters']} and the simulated readout circuit.