Research ArticlePHYSICS

Qubit parity measurement by parametric driving in circuit QED

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Science Advances  30 Nov 2018:
Vol. 4, no. 11, eaau1695
DOI: 10.1126/sciadv.aau1695
  • Fig. 1 Two-qubit parity measurement.

    (A) Qubit state–dependent frequency of the resonator. The parametric two-photon drive (orange) is resonant when the qubits are in the odd subspace, δo = 0 (blue), and strongly detuned when the qubits are in the even subspace, δe = ± 2χ (red). (B) Resonator phase space under two-photon driving. In the odd subspace, the resonator bifurcates in either ± αo (blue), while in the even subspace, it stays close to vacuum (red). The qubit parity is inferred by monitoring the amplitude of the field leaking out of the resonator. Inset: In the qubit even subspace, fluctuations are increased in a qubit state–dependent quadrature, leading to slow dephasing inside the subspace. (C) Possible circuit QED realization of the two-qubit parity measurement. Transmon qubits (red) are capacitively coupled to an off-resonant, nonlinear resonator (green).

  • Fig. 2 Measurement fidelity and concurrence.

    (A) Measurement fidelity as a function of time. (B) Concurrence conditioned on the measurement record being even (red) or odd (blue). The parameters are K/κ = 0.175, χ/κ = 25, and Embedded Image/κ = 2.5 for both panels.

  • Fig. 3 Four-qubit parity measurement.

    (A) Top: Nonlinear resonator qubit state–dependent frequency. A two-tone two-photon drive Embedded Image is sent to the resonator at δ = ± 2χ (orange double arrows). Bottom: Resonator photons are converted to a filter frequency (purple) via a two-tone coupling modulation g(t) (dark green). (B) Possible circuit QED realization. Transmon qubits (red) are capacitively coupled to a high-Q, nonlinear resonator (light green), which is coupled via a tunable coupler (dark green) to a low-Q filter mode (purple). A two-tone microwave drive on the nonlinear resonator (orange) induces the two-photon drive, while the coupling modulation is induced by the combination of a drive on the nonlinear resonator and a two-tone drive on the filter mode (dark green).

  • Fig. 4 Schematic for a possible circuit QED realization of the nine-qubit surface code.

    Qubits are represented by red circles, and out-of-plane interconnects are represented by squares. Single-qubit readout and control are achieved through the yellow resonators and brown lines, respectively. Parity measurements are performed using the circuit of Fig. 3B, here represented with half-wavelength nonlinear resonators. Embedded Image error syndromes are measured in light gray regions, while Embedded Image error syndromes are measured in dark gray regions.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/11/eaau1695/DC1

    Supplementary Text

    Fig. S1. Schematic representation of the steady state of a parametrically driven nonlinear resonator in parameter space.

    Fig. S2. Illustration of the resonator phase space when the qubits are in the even subspace.

    Fig. S3. Illustration of the resonator phase space when the qubits are in the odd subspace.

    Fig. S4. Possible circuit QED implementation of the two-qubit parity measurement.

    Fig. S5. A possible circuit QED implementation for the four-qubit parity measurement.

    Fig. S6. Fidelity of the two-qubit parity measurement as a function of measurement time for different decay times of the qubits.

    References (4347)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text
    • Fig. S1. Schematic representation of the steady state of a parametrically driven nonlinear resonator in parameter space.
    • Fig. S2. Illustration of the resonator phase space when the qubits are in the even subspace.
    • Fig. S3. Illustration of the resonator phase space when the qubits are in the odd subspace.
    • Fig. S4. Possible circuit QED implementation of the two-qubit parity measurement.
    • Fig. S5. A possible circuit QED implementation for the four-qubit parity measurement.
    • Fig. S6. Fidelity of the two-qubit parity measurement as a function of measurement time for different decay times of the qubits.
    • References (4347)

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