Dispersive readout of a flux qubit at the single-photon level

A superconducting flux qubit is inductively coupled to a superconducting quantum interference device (SQUID) magnetometer, capacitively shunted to form a 1.294-GHz resonator. The qubit-state-dependent resonator frequency is weakly probed with a microwave signal and detected with a microstrip SQUID amplifier. At a mean resonator occupation $\overline{n}=1.5$ photons, the readout visibility is increased by a factor of 4.5 over that using a cryogenic semiconductor amplifier. As $\overline{n}$ is increased from 0.008 to 0.1, no reduction in $T_1$ is observed, potentially enabling continuous monitoring of the qubit state.

Figure 1

False color optical micrograph of the qubit and readout resonator. A three-junction flux qubit is inductively coupled to a dc SQUID shunted by two parallel-plate capacitors in series, forming a tunable nonlinear resonator for qubit readout. The capacitors consist of aluminum films with a niobium underlayer, separated by a ${\text{SiN}}_x$ dielectric. Symmetric on-chip flux bias lines allow independent tuning of the qubit and SQUID, while a shorted CPW structure allows microwave excitation and fast flux tuning of the qubit.

Figure 2

Improvement in measurement sensitivity due to the MSA. The transmission data are normalized to a configuration with the MSA switched out of the measurement chain. At 1.294 GHz the MSA provides 27-dB gain (blue dots) with close to 10-MHz bandwidth. The increase in the output noise power (red dashes) is 17 dB, yielding an overall improvement in power SNR (increase in ratio of gain to output noise) of 10 dB (solid green line).

Figure 3

Schematic of cryogenic microwave measurement chain. A switch anchored to the mixing chamber stage allows the biased and operating MSA to be switched into/out of (thin/heavy dashed lines only) the readout circuit, allowing for a direct comparison of both configurations.

Figure 4

Visibility vs mean cavity photon occupation for the MSA switched into and out of the circuit. A visibility of 100$\%$ corresponds to the calculated maximum achievable fidelity limited by all factors except SNR. The error bars on the blue triangles are smaller than the markers.

Figure 5

Relaxation time constant ($T_1$) during readout vs mean cavity photon occupation.