Efficient and Low-Backaction Quantum Measurement Using a Chip-Scale Detector

Superconducting qubits are a leading platform for scalable quantum computing and quantum error correction. One feature of this platform is the ability to perform projective measurements orders of magnitude more quickly than qubit decoherence times. Such measurements are enabled by the use of quantum-limited parametric amplifiers in conjunction with ferrite circulators—magnetic devices which provide isolation from noise and decoherence due to amplifier backaction. Because these nonreciprocal elements have limited performance and are not easily integrated on chip, it has been a long-standing goal to replace them with a scalable alternative. Here, we demonstrate a solution to this problem by using a superconducting switch to control the coupling between a qubit and amplifier. Doing so, we measure a transmon qubit using a single, chip-scale device to provide both parametric amplification and isolation from the bulk of amplifier backaction. This measurement is also fast, high fidelity, and has 70% efficiency, comparable to the best that has been reported in any superconducting qubit measurement. As such, this work constitutes a high-quality platform for the scalable measurement of superconducting qubits.

Figure 1

Procedure. (a) A transmon qubit is measured using a “superconducting isolating modular bifurcation amplifier” (SIMBA). (b) The SIMBA is composed of a two-port parametric cavity with a tunable-inductor-bridge (TIB) style coupler on each port. (c) To measure the qubit, a probe tone is sent into the readout cavity, swapped into the parametric cavity, and then amplified. The amplified state is then coupled to a standard cryogenic measurement chain and digitized. Cyan (pink) histograms correspond to single-shot measurements when the qubit has been prepared in the ground (excited) state.

Figure 2

Calibration. (a) A uniform external flux is swept while probing the readout cavity in transmission with both TIBs in transmit mode. The avoided crossing shows the parametric cavity tuning through the readout cavity. To operate a SIMBA, this uniform flux bias is set so that the readout and parametric cavities are minimally detuned. (b) Readout fidelity $F_r$ (the ability of a measurement to distinguish the qubit eigenstate [75]) is plotted versus the duration for which TIB1 is set to transmit mode within the measurement sequence. Oscillations with a period of 40 ns indicate coherent swapping of a readout pulse between the readout and parametric cavities.

Figure 3

Characterization. (a) Postmeasurement qubit coherence $|{\widehat{\rho }}_{01}^{\prime }|$ is obtained by inserting a variable measurement into a Ramsey sequence, exposing the qubit to backaction. The ratio of the amplitude of the measured Ramsey fringes to the amplitude of those measured without this backaction (nothing inserted into the Ramsey sequence) equals $2|{\widehat{\rho }}_{01}^{\prime }|$. (b) Excess backaction is determined by inserting a “measurement” with zero readout amplitude. Postmeasurement coherence after excess backaction with the parametric cavity pump on (indigo) and off (cyan) are compared to a case with no backaction (no readout pulse, pump, or TIB switching inserted in the Ramsey sequence, violet). (c) Postmeasurement coherence $|{\widehat{\rho }}_{01}^{\prime }|$ (left $y$ axis) and readout fidelity $F_r$ (right $y$ axis, red data points) are measured while sweeping the readout amplitude $\sqrt{n_r}$ of a variable strength measurement. As in (b), $|{\widehat{\rho }}_{01}^{\prime }|$ is measured both with the parametric pump turned on or off during the variable measurement sequence (indigo or cyan data points, respectively). Postmeasurement coherence with the parametric pump turned on, but in the absence of readout photons, is specified by ${\rho }_b=|{\widehat{\rho }}_{01}^{\prime }(\sqrt{n_r}=0)|$ and determines the excess backaction $n_b=-\log (2{\rho }_b)/2$. Measurement efficiency $\eta$ is determined by a comparison between measurement-induced dephasing and readout fidelity while sweeping readout amplitude.