Single-Shot Single-Gate rf Spin Readout in Silicon

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Single-Shot Single-Gate rf Spin Readout in Silicon

P. Pakkiam, A. V. Timofeev, M. G. House, M. R. Hogg, T. Kobayashi, M. Koch, S. Rogge, and M. Y. Simmons

Phys. Rev. X 8, 041032 – Published 26 November 2018

Abstract

For solid-state spin qubits, single-gate rf readout can minimize the number of gates required for scale-up since the readout sensor can integrate into the existing gates used to manipulate the qubits. However, state-of-the-art topological error correction codes benefit from the ability to resolve the qubit state within a single shot, that is, without repeated measurements. Here, we demonstrate single-gate, single-shot readout of a singlet-triplet spin state in silicon, with an average readout fidelity of 82.9% at 3.3 kHz measurement bandwidth. We use this technique to measure a triplet $T_{-}$ to singlet $S_{0}$ relaxation time of 0.62 ms in precision donor quantum dots in silicon. We also show that the use of rf readout does not impact the spin lifetimes ( $S_{0}$ to $T_{-}$ decay remained approximately 2 ms at zero detuning). This establishes single-gate sensing as a viable readout method for spin qubits.

Received 10 September 2018
Revised 16 October 2018

DOI:https://doi.org/10.1103/PhysRevX.8.041032

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Spin blockade Spin-triplet pairing

Quantum dots

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

Authors & Affiliations

P. Pakkiam, A. V. Timofeev, M. G. House, M. R. Hogg, T. Kobayashi, M. Koch, S. Rogge, and M. Y. Simmons

Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, UNSW Sydney, New South Wales 2052, Australia

Popular Summary

Quantum bits (or qubits) made from single atoms in semiconductors are a promising platform for large-scale quantum computers, thanks to their long-lasting stability. To perform logic operations, two atom-size qubits must be placed very close together, which makes it challenging to squeeze in all the electrodes and sensors needed for qubit control and readout. One solution is to use the control electrodes not only for qubit manipulation but also for sensing the state of the qubit spin state by applying a small oscillating radio frequency (rf) electric field to the electrode. However, the sensitivity has not yet been high enough to measure electron spin states in real time. Here, we demonstrate a paradigm shift for scaling up semiconductor qubits that allows one to read an electron spin with one measurement (aka “single shot”) without the need to repeat the experiment and average the outcomes.

In our approach, an rf signal attempts to move pairs of electrons between dots, but this motion is only possible for certain combinations of electron spins. If the attempt is successful, the motion of charge drives a signal in a resonator attached to one of the gates. We show that this approach allows us to sense the spin state in a single shot with readout fidelities of 82%, and it does so without affecting the spin dynamics during the measurement.

This demonstration confirms that single-gate rf sensing of electron spins is reaching the sensitivity required to perform the necessary quantum error correction in a scalable quantum computer.

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Vol. 8, Iss. 4 — October - December 2018

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Images

Figure 1
Single-gate sensor readout with an integrated superconducting resonator circuit. (a) The STM image shows the silicon surface lithography where the lighter regions have been desorbed from the lithographic hydrogen mask. These areas are dosed with phosphorus to form the dots (D1U, D1L, D2U, and D2L) and metallic electrodes [25]. A standard chip inductor connects to the tunnel junction charge sensor TJ. Reservoir R2 is used to load dots D2L and D2U with electrons, while gates G1 and G2 are used to manipulate the singlet-triplet detuning of the dot pairs. The capacitors indicate the parasitic capacitance of the inductors. B indicates the in-plane magnetic field during millikelvin measurements. (b) The superconducting inductor is added to the frequency-multiplexed line, connected to R2, and it measures the singlet-triplet state across D2U and D2L. (c) The reflected (sending and receiving the rf tone via the multiplexed line) frequency response of the superconducting inductor when connected to R2 at zero magnetic field.
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Figure 2
Optimizing the singlet-triplet readout position. Using the sensor on R2, singlet states were time resolved to find the optimal point in detuning. (a) Charge stability diagram around the (2,4)-(3,3) transition taken by observing the differential rf amplitude response of the sensor TJ while sweeping gates G1 and G2 across a singlet-triplet transition on D2L and D2U. (b) The singlet-triplet energy diagram highlighting the $T_{-}$ ground state (blue) and the $S_{0} (1, 1)$ to $S_{0} (0, 2)$ crossing (red), where the electron oscillates when performing singlet readout. Note that $E_{z}$ is the Zeeman energy of the triplet $T_{\pm}$ states due to the applied 2.75 T magnetic field, while $Δ_{rf}$ denotes the amplitude of the rf tone. (c) Optimizing the rf amplitude $Δ_{rf}$ at 0 T to find the minimum amplitude that gives the signal maximum. The dotted lines fit the data with a Gaussian for visual clarity. (d) rf response at 2.75 T averaged over 10 000 shots at different points in detuning. Each trace was taken when waiting at L for 4.1 ms. The nonzero rf response signifies the presence of oscillating electrons (singlet states) that eventually decay into triplet $T_{-}$ states. (e) When fitting an exponential to each trace, it is clear that, at zero detuning, the rf response is maximal. (f) In all the experiments (a)–(d), the rf tone was constantly present. In this plot, we show the resulting rf response (fitted from the exponential $S_{0} − T_{-}$ decays as in (d) at zero detuning when turning on the rf pulse after a time waiting 0–3 ms at M. The resulting decay (shown in the inset) has the same time constant of 2 ms, suggesting that the decay is not an effect of applying the rf tone.
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Figure 3
Single-shot single-spin readout. Using the superconducting spiral inductor on our single-gate sensor R2, single spin states could be resolved with a single shot. (a) Single-shot traces (offset) measuring a single spin in the singlet state when waiting at L for 4.1 ms (shown in red) compared to those in triplet states where we did not pulse to L (shown in blue). (b) A histogram [a probability density function (PDF) from 10 000 traces] of the maximum value of the rf response when waiting at point L for 0 s and 4.1 ms shown in blue and red, respectively. The dashed line shows the selected threshold that maximizes the readout fidelity at 82.9%. (c) 500 individual time traces of the rf response. The first 250 were taken after waiting at L for 0.7 ms to partially load singlet states, and the second 250 traces were taken after waiting at L for 4.1 ms to fully load singlet states. The high rf response signifies the presence of singlet states that stochastically decay into triplet $T_{-}$ states. The shorter wait time highlights the lower singlet population, as insufficient time was given for the $T_{-}$ state to decay into the $S_{0}$ state before measurement. (d) To observe this dependence, using the optimal readout threshold, 1000 single-shot traces were taken to measure the singlet population on varying the time spent at point L. This probes the $T_{-}$ to $S_{0}$ relaxation time at $Δ \sim 1 meV$ of 0.62 ms.
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