Letter
https://doi.org/10.1038/s41586-019-1381-2
A two-qubit gate between phosphorus donor
electrons in silicon
Y. H e1,2, S. K. Gorman1,2, D. Keith^1 , L. Kranz^1 , J. G. Keizer^1 & M. Y. Simmons^1 *
Electron spin qubits formed by atoms in silicon have large (tens of
millielectronvolts) orbital energies and weak spin–orbit coupling,
giving rise to isolated electron spin ground states with coherence
times of seconds^1 ,^2. High-fidelity (more than 99.9 per cent) coherent
control of such qubits has been demonstrated^3 , promising an
attractive platform for quantum computing. However, inter-qubit
coupling—which is essential for realizing large-scale circuits in
atom-based qubits—has not yet been achieved. Exchange
interactions between electron spins^4 ,^5 promise fast (gigahertz) gate
operations with two-qubit gates, as recently demonstrated in gate-
defined silicon quantum dots^6 –^10. However, creating a tunable
exchange interaction between two electrons bound to phosphorus
atom qubits has not been possible until now. This is because it is
difficult to determine the atomic distance required to turn the
exchange interaction on and off while aligning the atomic circuitry
for high-fidelity, independent spin readout. Here we report a fast
(about 800 picoseconds) SWAP two-qubit exchange gate between
phosphorus donor electron spin qubits in silicon using independent
single-shot spin readout with a readout fidelity of about 94 per cent
on a complete set of basis states. By engineering qubit placement on
the atomic scale, we provide a route to the realization and efficient
characterization of multi-qubit quantum circuits based on donor
qubits in silicon.
Early proposals for spin qubits in semiconductors, such as those by
Kane^1 and Loss & DiVincenzo^5 , envisaged using large exchange inter-
actions J to couple neighbouring electron and/or nuclear spin qubits.
The exchange interaction generates a natural two-qubit gate by condi-
tionally swapping the electron spin states if they are anti-parallel.
Experimentally this requires tuning the exchange energy by many
orders of magnitude up to gigahertz frequencies over a relatively small
range in voltage detuning, making the realization of a SWAP gate chal-
lenging. Besides the SWAP gate, two other approaches to realizing a
two-qubit exchange gate in gate-defined quantum dots have been pur-
sued: the controlled phase (CZ)^11 and the controlled rotation (CROT)^12
operations. When combined with single-qubit rotations, any of these
three entangling gates are sufficient to perform universal quantum
computation. A quality unique to the SWAP gate is its capability to
move quantum information through large arrays of qubits that are only
coupled to their neighbours by performing multiple SWAP operations^4.
In particular, donor-based systems proposed by Kane^1 , with their
tight-confinement potential, minimal gate density^13 and strong capac-
itive coupling, have the potential of achieving strong exchange cou-
pling^14 for fast SWAP gates in quantum computing applications.
However, because of their small Bohr radius, it is difficult to determine
how far apart to place the qubits to tune the exchange interaction high
enough to perform a SWAP gate while still allowing independent
initialization and measurement when the exchange is low.
The first two-qubit gate demonstrated in silicon was a CZ gate per-
formed in isotopically pure^28 Si metal–oxide–semiconductor quantum
dots^6 , using magnetic control with an on-chip electron spin reso-
nance (ESR) antenna in 480 ns. By combining the CZ operation with
a single-qubit operation, a CNOT gate was realized in about 1.2 μs,
albeit without independent single-shot spin readout. Given that ESR
requires a strong oscillating magnetic field, Zajac et al.^7 pursued the
integration of a micromagnet in natSiGe (natSi, natural silicon) quantum
dots to use faster electrical pulses rather than magnetic control^15. As a
consequence, they demonstrated a CNOT gate via a single microwave
pulse (CROT) in about 200 ns (nearly an order of magnitude faster than
the CZ gate) with a 75% Bell state fidelity. In 2018, Watson et al.^8 , also
demonstrated a CNOT gate in natSiGe quantum dots using electrically
driven spin resonance (EDSR) within 280 ns with an average Bell state
fidelity of 85%–89% (after removing the readout errors on the qubits).
Recently, Huang et al.^10 used a CROT gate and ESR to generate Bell
states with an average fidelity of 85% within 1.4 μs, after removing
readout errors.
It is well known that the main source of decoherence when using the
exchange interaction is charge noise along the detuning axis between
two qubits^16. Nevertheless, Nowack et al.^17 were able to demonstrate
independent spin readout combined with sufficient control over the
exchange interaction to perform a SWAP operation in GaAs gate-
defined quantum dots. In this paper we present the first demonstration
of a SWAP two-qubit gate in silicon between independently meas-
ured electron spins bound to phosphorus donors in natural silicon. In
the long term, by combining the small size and excellent coherence
properties of atom-scale qubits in silicon, we aim to utilize the hallmark
long coherence times that are normally associated with ion trap qubits
together with the scalability of the silicon material system to realize a
large-scale quantum processor.
The two-qubit device (Fig. 1a) was fabricated using scanning tunnel-
ling microscopy (STM) hydrogen lithography for precision placement
of the donors and readout structures^18 ,^19 (see Methods). The qubits
are weakly tunnel-coupled to a radiofrequency single-electron tran-
sistor (RF-SET) that acts as a charge sensor and electron reservoir to
load the electrons onto the donor quantum dots (left (L) and right
(R); see Fig. 1b). Three electrical gates (left, middle and right) are
used to control the electrochemical potentials of the quantum dots,
whereas the SET gate is predominantly used to control the electro-
chemical potential of the RF-SET. The donor-based quantum dots con-
sist of separate clusters of 2P and 3P atoms for L and R, respectively,
determined by their charging energies (see Methods). The reasons
for atomically engineering asymmetry in the number of donors in
each quantum dot is to extend spin relaxation times^20 , mitigate spa-
tial exchange oscillations^21 and increase the tunability of the exchange
interaction^22. The device was measured in a dilution refrigerator with
a base temperature of 50 mK (see Methods) and a Zeeman energy of
EZ/h = γeB/2π ≈ 70 GHz (magnetic field B = 2.5 T; h, Planck’s con-
stant; γe, electron gyromagnetic ratio).
We use the (1, 3) electron charge states (where (nL, nR) are the elec-
tron numbers of L and R, respectively) to operate our qubits, where the
3P donor hyperfine energy is reduced by electronic shielding from the
inner electrons^23. The SWAP gate is performed at the (1, 3) ↔ (2, 2)
charge transition shown in Fig. 1c, which is equivalent to the(^1) Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales, Australia. (^2) These authors
contributed equally: Y. He, S. K. Gorman. *e-mail: [email protected]
18 JULY 2019 | VOL 571 | NAtUre | 371