Assessment of a Silicon Quantum Dot Spin Qubit Environment via Noise Spectroscopy

Preserving coherence long enough to perform meaningful calculations is one of the major challenges on the pathway to large-scale quantum-computer implementations. Noise coupled in from the environment is the main factor contributing to decoherence but can be mitigated via engineering design and control solutions. However, this is possible only after acquisition of a thorough understanding of the dominant noise sources and their spectrum. In the work reported here, we use a silicon quantum dot spin qubit as a metrological device to study the noise environment experienced by the qubit. We compare the sensitivity of this qubit to electrical noise with that of an implanted silicon-donor qubit in the same environment and measurement setup. Our results show that, as expected, a quantum dot spin qubit is more sensitive to electrical noise than a donor spin qubit due to the larger Stark shift, and the noise-spectroscopy data show pronounced charge-noise contributions at intermediate frequencies (2–20 kHz).

Figure 1

(a) Scanning electron micrograph of a $\mathrm{Si}\mathrm{MOS}$ qubit device identical to the one studied here. The quantum dot confinement gate (CB) is marked with a dotted white line. Each quantum dot is confined in a $40\times 40{\mathrm{nm}}^2$ area underneath gates G1–G3. (b) Cross section of (a) along the $y$ axis of the qubit marked with a red dot (not to scale). In this paper, we report on the data obtained from qubit Q1, formed underneath gate G1, as depicted by the red dot. (c) Charge-stability diagram of a double-quantum-dot system confined under gates G1 and G2. (d) Rabi-chevron map showing qubit spin-up probability as a function of ESR detuning frequency, $f-f_0$, and ESR pulse time, ${\tau }_{\mathrm{ESR}}$. Here the ESR frequency is $f_0=38.7765$ GHz, ${\mathbf{B}}_{\mathrm{dc}}=1.4$ T, and the applied source microwave power $P_{\mathrm{ESR}}=5$ dBm. From these results, we extract the electron Landé $g$ factor to be 1.9789.

Figure 2

Randomized benchmarking of Clifford gates to determine the control fidelity of our qubit. The performance of each Clifford gate is tested by interleaving them with random Clifford gates. The Clifford-gate control fidelity of this device is 99.83%. The data are vertically shifted by 0.5 per trace for clarity. All error bars represent 95% confidence intervals taken from the exponential fits used to extract the control fidelity.

Figure 3

(a) Qubit CPMG coherence time as a function of the number of refocusing pulses $N$. The maximum $T_2^{\mathrm{CPMG}}$ is 6.7 ms as shown by the data point marked with a cross. (b) Noise spectrum of a $\mathrm{Si}\mathrm{MOS}$ quantum dot spin qubit. The noise power spectral density $S(\omega )$ is calculated from the $T_2^S$ data fitted to an exponential decay of the form $P(t)=P_0\exp [(-t/T_2^S{)}^n]+P_{\mathrm{\infty }}$ for different wait times ${\tau }_w$ between the $Y_{\pi }$ pulses. We observe a colored noise spectrum with an exponent of $\alpha =-2.5$ for $f<2$ kHz. At intermediate frequencies ($f=2-20\mathrm{kHz}$), our noise is dominated by an exponent of $\alpha =-0.8$ to $-1$, very close to $1/f$, which we attribute to charge noise. We also observe a pronounced peak in the spectrum at $f\approx 3.6$ kHz, which is caused by measurement electronics. At high frequencies ($f>20$ kHz), our white-noise floor is $350{\mathrm{rad}}^2/\mathrm{s}$. All error bars represent 95% confidence intervals from the exponential fits used to extract the decay times.

Figure 4

(a) Stark shift experienced by qubit G1 as a function of G1 and G2 gate voltages. The ESR frequencies are measured at different gate spaces with 8-mV step size and are extrapolated linearly as shown in the two-dimensional map. Here $f_0=38.7765$ GHz. From the results, we fit the qubit G1 Stark shift to be $df/d{V}_{\mathrm{G1}}=-36.21$ MHz/V and $df/d{V}_{\mathrm{G2}}=-22.88$ MHz/V. (b) CPMG noise spectrum obtained with application of a $20$-kHz sinusoidal tone as a function of its amplitude on gate G2 on the $y$ axis. The $x$ axis is translated into frequency from the CPMG wait time, and all data are taken with a fixed total precession time. The results elucidate significantly lower spin-up probability at a tone frequency starting from $160\mu V$ peak to peak. This is a verification of our noise-spectroscopy measurement technique and setup.

Figure 5

(a) Measured noise spectrum of the Stanford Research Systems SIM928 dc voltage source used to bias the qubit device. (b) Enlargement of the green region in (a) showing the noise spectrum in the 1–10-kHz range. The inset shows an enlargement of the noise spectrum of Q1 measured with more data points to exemplify the $1/f$ charge-noise trend and corroborate the peak at $f\approx 3.6$ kHz. The plot has the same frequency axis as the SIM928 noise spectrum, showing the matching noise peak at 3.6 kHz.