Research ArticleCONDENSED MATTER PHYSICS

A fault-tolerant addressable spin qubit in a natural silicon quantum dot

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Science Advances  12 Aug 2016:
Vol. 2, no. 8, e1600694
DOI: 10.1126/sciadv.1600694
  • Fig. 1 Device structure and EDSR measurement result.

    (A) False-color scanning electron micrograph of the device. The orange boxes represent ohmic contacts that are grounded during the measurements except for the one connected to the resonance circuit. The two small circles show the approximate position of the double quantum dot, and the large circle shows the approximate position of the sensor quantum dot. Three of the gate electrodes (R, L, and C) are connected to impedance-matched high-frequency lines with cryogenic bias tees. (B) Schematic of the pulse sequence used for the EDSR measurement. The pulse sequence consists of four stages, namely, initialization, control, readout, and emptying. (C) Charge stability diagram in the vicinity of the (1,1) charge configuration. MR,IR (ML,IL) denote the measurement and initialization points for the right (left) quantum dot. O denotes the operation point that is common for both right and left quantum dots. a.u., arbitrary units. (D) Measurement of the EDSR signal as a function of fMW and Bext. The blue line corresponds to the left dot resonance condition hfMW = gμ(Bext + Embedded Image), and the red line corresponds to the right dot resonance condition hfMW = gμ(Bext + Embedded Image). (E) Rabi oscillation with Embedded Image ~ 8 μs and fRabi ~ 9 MHz measured at Bext = 0.505 T and fMW = 15.6055 GHz. The red triangles show measurement data, and the black solid line shows the fitting with an exponentially damped sine curve, Embedded Image with A, B, fRabi, θ, and Embedded Image as fitting parameters. (F) Measurement result of detuned Rabi oscillations, which shows a typical chevron pattern.

  • Fig. 2 Ramsey interference measurements.

    (A) Schematic of the Ramsey measurement sequence. ϕ denotes the phase of the second microwave burst relative to the first Xπ/2 rotation. A rectangle or Gaussian microwave burst is applied to gate C. (B) Ramsey fringes measurement result. Bext is fixed at 0.505 T. ϕ is the phase of the second microwave burst relative to the first microwave burst. (C) Ramsey fringes decay envelope extracted by sweeping fMW at each fixed tw. The black solid line is a fit with a Gaussian decay function Embedded Image, where A and B are constants to account for the measurement and initialization fidelities. (D) Demonstration of the π/2 pulse around an arbitrary rotation axis in the xy plane of the Bloch sphere.

  • Fig. 3 Rabi oscillation power dependence.

    (A) Microwave amplitude dependence of Rabi oscillations measured at Bext = 0.505 T and fMW = 15.6055 GHz. (B) Microwave amplitude dependence of the Rabi frequency fRabi. The red triangles show the measured data, and the black dotted line shows a linear fitting for the small-amplitude data (0.1 ≤ AMW ≤ 0.25). The fitting error is smaller than the size of the symbols. (C) Microwave amplitude dependence of the Rabi decay time Embedded Image. Because the total evolution time of the data used for the fitting is relatively short (tp = 3 μs), it shows large errors for small AMW points. (D) Microwave amplitude dependence of the quality factor Embedded Image. The error mainly comes from the uncertainty of Embedded Image.

  • Fig. 4 Randomized benchmarking measurement.

    (A) Schematic of the randomized benchmarking sequence. The upper panel is a reference sequence consisting of m random Clifford gates. The lower panel is the interleaved sequence used to measure fidelities of a specific test Clifford gate Ctest. The sequence is repeated for k = 16 choices of sequences to obtain one point. (B) Reference randomized benchmarking for two different microwave amplitudes. The inset shows the quality factor measurement for Gaussian microwave burst, which shows a result that is similar to the one for rectangle microwave burst. (C) Interleaved randomized benchmarking for single-step Clifford gates. The table on the right shows fidelity measurement results for several single-qubit gates. The fitting error of each gate fidelity is smaller than 0.1% for the reference and all interleaving measurements.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/8/e1600694/DC1

    section S1. Sample structure and micromagnet simulation

    section S2. Measurement setup

    section S3. Right dot measurement data

    section S4. Discussions on the microwave power dependence

    section S5. Randomized benchmarking

    fig. S1. Micromagnet design and simulation.

    fig. S2. Single-shot spin readout using energy selective readout technique.

    fig. S3. Rabi oscillation and Ramsey measurements of the right quantum dot.

    fig. S4. Fitting of Rabi oscillation data.

    fig. S5. Rabi decay measurement for two different operation points.

    References (2831)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Sample structure and micromagnet simulation
    • section S2. Measurement setup
    • section S3. Right dot measurement data
    • section S4. Discussions on the microwave power dependence
    • section S5. Randomized benchmarking
    • fig. S1. Micromagnet design and simulation.
    • fig. S2. Single-shot spin readout using energy selective readout technique.
    • fig. S3. Rabi oscillation and Ramsey measurements of the right quantum dot.
    • fig. S4. Fitting of Rabi oscillation data.
    • fig. S5. Rabi decay measurement for two different operation points.
    • References (2831)

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