Fast Gate-Based Readout of Silicon Quantum Dots Using Josephson Parametric Amplification

S. Schaal, I. Ahmed, J. A. Haigh, L. Hutin, B. Bertrand, S. Barraud, M. Vinet, C.-M. Lee, N. Stelmashenko, J. W. A. Robinson, J. Y. Qiu, S. Hacohen-Gourgy, I. Siddiqi, M. F. Gonzalez-Zalba, and J. J. L. Morton

Phys. Rev. Lett. 124, 067701 – Published 14 February 2020

Abstract

Spins in silicon quantum devices are promising candidates for large-scale quantum computing. Gate-based sensing of spin qubits offers a compact and scalable readout with high fidelity, however, further improvements in sensitivity are required to meet the fidelity thresholds and measurement timescales needed for the implementation of fast feedback in error correction protocols. Here, we combine radio-frequency gate-based sensing at 622 MHz with a Josephson parametric amplifier, that operates in the 500–800 MHz band, to reduce the integration time required to read the state of a silicon double quantum dot formed in a nanowire transistor. Based on our achieved signal-to-noise ratio, we estimate that singlet-triplet single-shot readout with an average fidelity of 99.7% could be performed in $1 μ s$ , well below the requirements for fault-tolerant readout and 30 times faster than without the Josephson parametric amplifier. Additionally, the Josephson parametric amplifier allows operation at a lower radio-frequency power while maintaining identical signal-to-noise ratio. We determine a noise temperature of 200 mK with a contribution from the Josephson parametric amplifier (25%), cryogenic amplifier (25%) and the resonator (50%), showing routes to further increase the readout speed.

Received 23 July 2019
Accepted 17 January 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.067701

Physics Subject Headings (PhySH)

Quantum information processing Radio frequency techniques

Quantum dots Superconducting devices

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Schaal ^1,*, I. Ahmed^2,‡, J. A. Haigh³, L. Hutin⁴, B. Bertrand⁴, S. Barraud⁴, M. Vinet⁴, C.-M. Lee⁵, N. Stelmashenko⁵, J. W. A. Robinson⁵, J. Y. Qiu^6,§, S. Hacohen-Gourgy⁶, I. Siddiqi⁶, M. F. Gonzalez-Zalba³, and J. J. L. Morton^1,7,†

¹London Centre for Nanotechnology, University College London, London WC1H 0AH, United Kingdom
²Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
³Hitachi Cambridge Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
⁴CEA, LETI, Minatec Campus, F-38054 Grenoble, France
⁵Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
⁶Quantum Nanoelectronics Laboratory, Department of Physics, University of California, Berkeley California 94720, USA
⁷Department of Electronic & Electrical Engineering, University College London, London WC1E 7JE, United Kingdom

^*simon.schaal.15@ucl.ac.uk
^†jjl.morton@ucl.ac.uk
^‡Present address: Department of Electrical & Electronic Engineering, University of Dhaka, Dhaka 1000, Bangladesh.
^§Present address: Massachusetts Institute of Technology, Cambridge, MA 02139, USA.

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Vol. 124, Iss. 6 — 14 February 2020

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Images

Figure 1
Setup and Josephson parametric amplifier (JPA). (a) Schematic of the quantum dot readout setup consisting of microwave components (including a JPA), readout resonator, and CMOS quantum dot device (false-colored scanning electron microscope micrograph). (b) Phase response of the JPA as a function of flux bias $I_{bias}$ demonstrating frequency tuning of the JPA. (c) JPA phase response as a function pump power and frequency. The regime of parametric amplification and the readout resonator are indicated. (d) JPA transfer function obtained from linecuts at indicated frequencies in (c). The bistable regime is observed as an abrupt jump in $ϕ$ .
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Figure 2
Characterizing the $L C$ resonator and its operation with the JPA. (a) Shows the resonant circuit, including a schematic of the printed circuit board components and bond wires, the NbN spiral inductor, and the quantum dot device on a separate chip. (b) Magnitude and phase of the reflection coefficient showing the readout resonator ( $Q_{load} = 966$ ). (c) Gain profile of the JPA when tuned close to the readout resonator frequency (3-dB bandwidth of 6 MHz). (d) JPA gain and estimated system noise temperature at $f_{rf}$ as a function of rf input power showing saturation at high input power (1-dB compression at $- 121 dBm$ ).
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Figure 3
Dot-to-reservoir transition (DRT) charge sensitivity. (a) Schematic cross section of the QD devices along the gate, and (b) along the source and drain, showing two QDs in the top corners of the nanowire and a donor in the channel. Transitions at which measurements are performed are indicated. (c) Typical phase response across a DRT ( $P_{rf} = - 125 dBm$ ). (d) Full width at half maximum (FWHM) of the DRT as a function of power (power broadened at $P_{rf} > 110 dBm$ ). (e) SNR of the DRT as a function of rf power. The power at which the JPA saturates (dashed line) and significant power broadening occurs (dotted line) is indicated.
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Figure 4
Inter–donor-dot charge transition (IDT). (a) Even-parity IDT between a donor and QD in the device. Electron occupation ( $N_{dot}$ , $N_{donor}$ ) indicated, up to an arbitrary offset. (b) Normalized phase response along the detuning axis $ϵ$ in (a) with and without the JPA for two different integration times (traces offset by 1.5 in $Δ ϕ$ for clarity). (c) SNR obtained from traces as shown in (b) as a function of integration time with JPA on and off. Linear extrapolation and $SNR = 1$ is indicated using dotted lines. (d) Simulated average readout infidelity $1 - F_{avg}$ as a function of $τ_{int}$ . The horizontal dotted line indicates $F_{avg} = 0.997$ .
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