Nature - USA (2019-07-18)

reSeArCH Letter

through optimizing device fabrication processes (see Supplementary
Information section III). In the future, by using single-qubit rotations
in the rotated basis we will be able to extract the overall two-qubit gate
fidelity. This will require transitioning to devices made in isotopically
purified^27 28 Si, in which high-fidelity single-qubit gates have been
demonstrated^2.
The results presented in this paper demonstrate the first two-qubit
gate for coupled donor atom qubits in silicon. The SWAP gate fidelity
in the z basis, Fzz,S=±90% 3% is ultimately limited by charge noise
along the detuning axis of the qubits, which controls the strength of the
exchange interaction^28. Several methods have been proposed to reduce
charge noise, such as using symmetric gate operations^29 , applying com-
posite pulse sequences^30 and designing a device with separated RF-SET
and electron reservoir to reduce back-action of the charge sensor^31.
These possibilities, combined with the recently demonstrated
low charge noise in buried planar devices compared with other two-
dimensional materials^32 and methodologies to improve device crystal-
linity^33 , bode well for donor-based SWAP gates. Future experiments
will focus on measuring the Bell states obtained using the SWAP gate
to demonstrate entanglement between two electrons using isotopically
purified^28 Si.

Online content
Any methods, additional references, Nature Research reporting summaries, source
data, statements of data availability and associated accession codes are available at
https://doi.org/10.1038/s41586-019-1381-2.

Received: 22 October 2018; Accepted: 28 May 2019;

Published online 17 July 2019.

1. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393 ,
   133–137 (1998).


2. Muhonen, J. T. et al. Storing quantum information for 30 seconds in a
   nanoelectronic device. Nat. Nanotechnol. 9 , 986–991 (2014).


3. Muhonen, J. T. et al. Quantifying the quantum gate fidelity of single-atom spin
   qubits in silicon by randomized benchmarking. J. Phys. Condens. Matter 27 ,
   154205 (2015).


4. Hill, C. D. et al. Global control and fast solid-state donor electron spin quantum
   computing. Phys. Rev. B 72 , 045350 (2005).


5. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys.
   Rev. A 57 , 120–126 (1998).


6. Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526 , 410–414
   (2015).


7. Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359 ,
   439–442 (2018).


8. Watson, T. F. et al. A programmable two-qubit quantum processor in silicon.
   Nature 555 , 633–637 (2018).


9. Brunner, R. et al. Two-qubit gate of combined single-spin rotation and
   interdot spin exchange in a double quantum dot. Phys. Rev. Lett. 107 , 146801
   (2011).


10. Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569 ,
    532–536 (2019).


11. Meunier, T., Calado, V. E. & Vandersypen, L. M. K. Efficient controlled-phase gate
    for single-spin qubits in quantum dots. Phys. Rev. B 83 , 121403 (2011).


12. Kalra, R., Laucht, A., Hill, C. D. & Morello, A. Robust two-qubit gates for donors in
    silicon controlled by hyperfine interactions. Phys. Rev. X 4 , 021044 (2014).


13. Hile, S. J. et al. Radio frequency reflectometry and charge sensing of a precision
    placed donor in silicon. Appl. Phys. Lett. 107 , 093504 (2015).


14. Weber, B. et al. Spin blockade and exchange in Coulomb-confined silicon
    double quantum dots. Nat. Nanotechnol. 9 , 430–435 (2014).

Two-spin probabilities

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Two-spin probabilities

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Fig. 4 | Two-qubit SWAP gate with truth table. a, b, Pulse sequence for
performing a SWAP gate using a voltage pulse with a rise time of
about 100 ps. The different input states are initialized by varying
the loading position on each qubit (see Supplementary Information
section IV). c–f, Measured two-spin probabilities in the basis
{∣⟩∣⟩∣⟩∣⟩↓↓,,,}↑↓ ↓↑ ↑↑ with initial states ρ↓↓=↓∣⟩↓↓⟨∣↓,
ρ↑↓=↑()∣⟩↓↑⟨∣↓+∣⟩↓↓ ↓↓⟨∣/ 2 , ρ↓↑=↓()∣⟩↑↓⟨∣↑+∣⟩↓↓ ↓↓⟨∣/ 2 and
ρRR=↑()∣⟩↑↑⟨∣↑+∣⟩↑↓ ↑↓⟨∣+↓∣⟩↑↓⟨∣↑+∣⟩↓↓ ↓↓⟨∣/ 4 , respectively. All
data are measured with an exchange coupling of Ω/2π ≈  300  MHz

(second trace from the top in Fig. 3d). In c and e, the solid blue and red

lines are the fits to P↑↓ and P↓↑. g, Results (E) of the truth tables of the

SWAP, SWAP and SWAP^2 gates compared with the corresponding ideal

cases (T). The SWAP data are extracted from the two-spin probabilities

at the π/2 exchange oscillation (t = 0.77 ns), as indicated by the dotted

line labelled S in c, e. The SWAP gate (S in c, e) is completed after a π

oscillation at t = 1.54 ns. Finally, the full 2π oscillation (S^2 in c, e) occurs

at t = 3.08 ns, which results in an identity operation. The error bars

represent uncertainty of one standard deviation in the measured values.

374 | NAtUre | VOL 571 | 18 JULY 2019