A two-qubit logic gate in silicon

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Quantum computation requires qubits that can be coupled in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates1, 2. Many physical realizations of qubits exist, including single photons3, trapped ions4, superconducting circuits5, single defects or atoms in diamond6, 7 and silicon8, and semiconductor quantum dots9, with single-qubit fidelities that exceed the stringent thresholds required for fault-tolerant quantum computing10. Despite this, high-fidelity two-qubit gates in the solid state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits5, owing to the difficulties of coupling qubits and dephasing in semiconductor systems11, 12, 13. Here we present a two-qubit logic gate, which uses single spins in isotopically enriched silicon14 and is realized by performing single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the Loss–DiVincenzo proposal2. We realize CNOT gates via controlled-phase operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is used in the two-qubit controlled-phase gate. By independently reading out both qubits, we measure clear anticorrelations in the two-spin probabilities of the CNOT gate.

At a glance


  1. Silicon two-qubit logic device, incorporating SET read-out and selective qubit control.
    Figure 1: Silicon two-qubit logic device, incorporating SET read-out and selective qubit control.

    a, b, Schematic (a) and scanning electron microscope coloured image (b) of the device. The quantum dot structure (labels GC and G1–4) can be operated as a single or double quantum dot by appropriate biasing of gate electrodes G1–G4, where we choose here to confine the dots D1,2 underneath gates G1,2, respectively. The confinement gate GC runs underneath G1–G3 and confines the quantum dot on all sides except on the reservoir (R) side. Qubit operation is achieved via an ac current Iac through the ESR line, resulting in an ac magnetic field Bac. c, Stability diagram of the double quantum dot obtained by monitoring the current ISET through the capacitively coupled SET. The numbers in parentheses are the change occupancies of D2,1: (N2, N1). The difference in distance to the SET results in different capacitive coupling, such that the individual dots can be easily distinguished. The tunnel coupling of the fourth transition (N1 = 3 right arrow 4) of D1 is relatively weak, which is due to valley and spin filling, because there is only one state in the lowest orbital that can be occupied. Q1 and Q2 are realized by depleting D1 and D2 to the last electron. d, The quantum dot qubits can be individually controlled by electrically tuning the ESR resonance frequency using the Stark shift9. Clear Rabi oscillations for both qubits are observed. All measurements were performed in a dilution refrigerator with base temperature T 50 mK and a dc magnetic field of strength B0 = 1.4 T.

  2. Exchange spin funnel.
    Figure 2: Exchange spin funnel.

    a, Close up of the operation regime of the (1, 1)–(0, 2) charge states. We lowered the R–D2 coupling so that the tunnelling time is approximately 100 μs, matching the qubit experiments. In this range of weak R–D1 coupling, the emptying and filling of D1 is hysteretic with gate voltage, because the mutual charging energy becomes relevant27, as D1 can only tunnel when it aligns in energy with D2. R2 represents the read-out on Q2; IAP represents the antiparallel initialization. b, Schematic of the coupling between Q1 and Q2 using the exchange interaction at the |1, 1right fence–|0, 2right fence transition. By electrically tuning the g factors9 of Q1 and Q2, we control the individual qubit resonance frequencies over 10 MHz. Here, we tune to a frequency difference of 40 MHz (the difference is exaggerated in the schematic for clarity) for individual qubit control. c, ESR spectrum of the |↓, ↓right fence–|↑, ↓right fence transition as a function of increasing detuning. The data have been offset by a frequency ν0 = 39.14 GHz and the spin-up fractions are normalized for clarity. The dashed lines are fits using equation (1) and assuming t0 = 900 MHz, a Stark shift of 19 MHz V−1, and that the top gates have a lever arm of 0.2 eV V−1. d, As for c, but with an additional pulse of amplitude VAP (see schematic) so that we initialize antiparallel spin states (AP) and observe both the |↑, ↓right fence–|↓, ↓right fence and |↓, ↑right fence–|↑, ↑right fence transitions. The labels I–IV indicate electron tunnelling between R and D1,2; see text for details.

  3. Controlled phase (CZ) gate operation time.
    Figure 3: Controlled phase (CZ) gate operation time.

    a, Spin-up fraction after applying a (π/2)X-pulse, a CZ operation and a (π/2)Y-pulse, for increasing qubit interaction. The exchange coupling is controlled via ϵ, set with , resulting in a tunable two-qubit operation frequency ν↑↓. b, By fitting the data in a, we map out ν↑↓ and as a function of VCZ. The orange and blue colouring and the arrows indicate the axis each data set corresponds to; the colouring of the data corresponds to that in c, indicating VCZ. The inset shows the number of possible CZ rotations NCZ. Although decreases with coupling, the number of possible two-qubit rotations continues to increase.

  4. Two-spin correlations for a two-qubit logic gate.
    Figure 4: Two-spin correlations for a two-qubit logic gate.

    a, Pulsing protocol for two-qubit read-out and single- and two-qubit operations. After read-out of Q2 (R2) and Q1 (R1), we pulse back to (R2) to ensure proper initialization. Individual qubit operations are performed with high ϵ, whereas the CZ operation occurs in the presence of interaction. b, Stability diagram showing the operation regime. c, Spin-up fraction of both qubits after initializing Q1 spin up (top) and spin down (bottom) using a microwave pulse and applying a controlled rotation using Q2 as the target qubit. A CNOT gate is achieved in 480 ns, as indicated by the dotted purple line (see inset for the corresponding Bloch sphere animation). d, Two-spin probabilities as functions of the microwave pulse length on Q1 after applying a CNOT gate (see inset for the corresponding Bloch sphere animation), showing clear anticorrelations between the two qubit spin states. The different plots correspond to different spin states of Q1,2, as indicated. The black lines correspond to fits based on a CNOT gate, and include the experimental read-out errors (see Supplementary Information section 9). The green dotted lines correspond to the intended maximally entangled states.


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Author information


  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

    • M. Veldhorst,
    • C. H. Yang,
    • J. C. C. Hwang,
    • W. Huang,
    • J. P. Dehollain,
    • J. T. Muhonen,
    • S. Simmons,
    • A. Laucht,
    • F. E. Hudson,
    • A. Morello &
    • A. S. Dzurak
  2. School of Fundamental Science and Technology, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

    • K. M. Itoh


M.V., C.H.Y. and J.C.C.H. performed the experiments. M.V. and F.E.H. fabricated the devices. K.M.I. prepared and supplied the 28Si epilayer wafer. W.H., J.P.D., J.T.M., S.S and A.L. contributed to the preparation of the experiments. M.V., C.H.Y., A.M. and A.S.D. designed the experiment and discussed the results. M.V. analysed the results. M.V. and A.S.D. wrote the manuscript with input from all co-authors.

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The authors declare no competing financial interests.

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Supplementary information

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  1. Supplementary Information (759 KB)

    This file contains Supplementary Methods, Text and Data, Supplementary Figures 1-7 and Supplementary References.

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