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

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Assessment of a Silicon Quantum Dot Spin Qubit Environment Via Noise Spectroscopy PHYSICAL REVIEW APPLIED 10, 044017 (2018) Assessment of a Silicon Quantum Dot Spin Qubit Environment via Noise Spectroscopy K. W. Chan,1,* W. Huang,1 C. H. Yang,1 J. C. C. Hwang,1 B. Hensen,1 T. Tanttu,1 F. E. Hudson,1 K. M. Itoh,2 A. Laucht,1 A. Morello,1 and A. S. Dzurak1,† 1 Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales 2052, Australia 2 School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan (Received 24 May 2018; revised manuscript received 6 July 2018; published 5 October 2018) 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). DOI: 10.1103/PhysRevApplied.10.044017 I. INTRODUCTION diamond-nitrogen-vacancy-center [14] qubits. Noise spec- troscopy for spin-based quantum computing in silicon Spin-based quantum dot qubits [1] in semiconductors has been performed for an implanted phosphorus-donor show promise for scalable quantum-information process- in silicon (Si:P) [2] qubit and a SiGe quantum dot ing due to their compatibility with well-established semi- [6] spin qubit. Here we use a silicon metal-oxide- conductor manufacturing technologies. Extremely long semiconductor (SiMOS) quantum dot spin qubit as a probe electron spin-coherence times have been demonstrated to enable noise spectroscopy via Carr-Purcell-Meiboom- in spin qubits fabricated on isotopically purified silicon Gill (CPMG) dynamical decoupling pulse sequences [15, [2–5], with control and read-out fidelities exceeding fault- 16]. We start by comprehensive characterization of the tolerance thresholds [3,6]. Two-qubit logic gates [7–10] qubit, which includes coherence-time measurements and based on silicon quantum dots have also been demon- randomized benchmarking of the single-qubit Clifford-gate strated as a consequence of these advancements. Scal- control fidelities. ing up to larger multiqubit systems, however, requires a more-stringent engineering of the qubits’ electromagnetic II. DEVICE ARCHITECTURE AND environment such that the collective fault-tolerance thresh- CHARACTERIZATION old is maintained for the implementation of surface code error-correction protocols [11]. This demands a detailed Figure 1(a) shows a scanning electron micrograph of understanding of the possible sources of noise that cause an identical device fabricated on an isotopically enriched decoherence at the very least. 900-nm 28Si epilayer [17] with an 800-ppm residual Noise spectroscopy is a valuable and necessary tool concentration of 29Si. This device is fabricated on the in building understanding of the noise sources present. basis of our previously reported aluminium-gate-stacked As part of the effort toward scaling up qubit sys- architecture [18,19], with the distinction of using bilayer tems, noise spectroscopy measurement has been under- PMMA/copolymer resist to ease the metal liftoff process. taken for superconducting [12], ion-trap [13]and The single-electron transistor (SET) is a charge sensor [20] used to read out the charge occupancy and electron spin state of the confined quantum dots under gates G1–G3. *[email protected] Gate GT acts as a tunnel barrier for the loading of elec- †[email protected] trons into the quantum dots from the reservoir gate (RES). 2331-7019/18/10(4)/044017(7) 044017-1 © 2018 American Physical Society K. W. CHAN et al. PHYS. REV. APPLIED 10, 044017 (2018) (a) (b) (c) (d) FIG. 2. Randomized benchmarking of Clifford gates to deter- mine the control fidelity of our qubit. The performance of each Clifford gate is tested by interleaving them with random Clif- FIG. 1. (a) Scanning electron micrograph of a SiMOS qubit ford gates. The Clifford-gate control fidelity of this device is device identical to the one studied here. The quantum dot con- 99.83%. The data are vertically shifted by 0.5 per trace for clar- finement gate (CB) is marked with a dotted white line. Each ity. All error bars represent 95% confidence intervals taken from quantum dot is confined in a 40 × 40 nm2 area underneath gates the exponential fits used to extract the control fidelity. 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, electrons under gate G1 (G2). In this experiment, the as depicted by the red dot. (c) Charge-stability diagram of a double dot is effectively configured as a single dot by double-quantum-dot system confined under gates G1 and G2. (d) operating near the (0, 0)–(1, 0) charge transition. The qubit Rabi-chevron map showing qubit spin-up probability as a func- Q1 control (C) and read-out (R) positions are labeled tion of ESR detuning frequency, f − f0, and ESR pulse time, τ . Here the ESR frequency is f = 38.7765 GHz, B = 1.4 T, in red. Detailed reports on the ESR measurement tech- ESR 0 dc nique and setup are presented in Ref. [3]. The measured and the applied source microwave power PESR = 5 dBm. From these results, we extract the electron Landé g factor to be 1.9789. Rabi-chevron pattern is depicted in Fig. 1(d). The high- quality chevron shows excellent control of the electron spin, with an extracted π-pulse time of 1.28 μs. With Gates G1–G3 are used to tune the electron occupancies. use of the single-shot spin to charge conversion technique [20,21], all experimental data shown are obtained with A dc magnetic field Bdc of 1.4 T is applied to Zeeman split the electron spin states to form the qubit eigen- the electron-reservoir tunnel rate tuned to approximately μ states. The electron spin state is manipulated by use of 100 s with at least 100 single-shot measurements for the electron-spin-resonance (ESR) microwave line to pro- each data point. For this qubit, we measure a spin relax- ≈ duce a perpendicular ac magnetic field B at microwave ation time T1 1 s and a Ramsey [22] dephasing time ac ∗ = ± μ frequency f . The directions of both magnetic fields, B T2 33 8 s (data not shown). In addition, we measure 0 dc H = ± μ and B , are indicated in Fig. 1(a). Figure 1(b) shows a the routinely reported coherence times T2 401 42 s, ac CP = ± = CPMG = ± schematic cross section of the device along the y axis of T2 1.5 0.2 ms (N 7 pulses), and T2 6.7 = the qubit, marked with a red dot in Fig. 1(a).Thered 2.9 ms (N 122 pulses) using Hahn echo [23], Carr- region underneath the reservoir gate illustrates a 2DEG Purcell [24], and Carr-Purcell-Meiboom-Gill [25] pulse formed with positive bias voltage, and extends to a nearby sequences, respectively. phosphorus-doped ohmic region. Figure 1(c) depicts the stability diagram showing the III. RANDOMIZED BENCHMARKING charge transitions on a double-dot system that is electro- statically confined under gates G1 and G2. The electron We perform randomized benchmarking [26]ofClif- occupancies are labeled in each Coulomb blockaded region ford gates to determine our control fidelity using standard as (N1,N2), with N1 (N2) representing the number of microwave square pulses as part of the characterization. 044017-2 ASSESSMENT OF A SILICON QUANTUM... PHYS. REV. APPLIED 10, 044017 (2018) (a) (b) CPMG FIG. 3. (a) Qubit CPMG coherence time as a function of the number of refocusing pulses N. The maximum T2 is 6.7 ms as shown by the data point marked with a cross. (b) Noise spectrum of a SiMOS quantum dot spin qubit. The noise power spectral (ω) S ( ) = (− / S)n + density S is calculated from the T2 data fitted to an exponential decay of the form P t P0exp[ t T2 ] P∞ for different wait times τw between the Yπ pulses. We observe a colored noise spectrum with an exponent of α =−2.5 for f < 2 kHz. At intermediate frequencies (f = 2–20 kHz), our noise is dominated by an exponent of α =−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 ≈ 3.6 kHz, which is caused by measurement electronics. At high frequencies (f > 20 kHz), our white-noise floor is 350 rad2/s. All error bars represent 95% confidence intervals from the exponential fits used to extract the decay times. Figure 2 displays the converted spin-up probability to con- corresponding pulse sequences are shown at the bottom trol fidelity as a function of the number of Clifford-gate right, with Yπ denoting a π rotation on the y axis of the operations M.
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