reSeArCH Letter
(1, 1) ↔ (2, 0) transition with an inactive singlet state on R. At this
higher charge transition we have a faster tunnel rate from the SET res-
ervoir to the quantum dots so we can minimize the sequential spin
readout time, enabling the collection of more statistics for mapping out
the exchange oscillations. Single-shot electron spin measurements are
performed using energy-selective readout^24 on each quantum dot. Spin
readout relies on aligning the SET Fermi level between spin up ()∣⟩↑
and spin down ()∣⟩↓ energy; see Fig. 1d. If the electron is spin-up, then
it will tunnel to the reservoir and cause a dip in the RF-SET signal. A
new electron in the spin-down state will then tunnel onto the quantum
dot and the RF-SET response will return to the idle value (D^0 -style
readout). If the electron is initially spin-down, then no tunnel events
will occur and the response of the RF-SET sensor will not dip. A similar
process is used on L, where, instead of unloading an electron, we
conditionally load an electron onto the quantum dot, which produces
the same response in the SET (D−-style readout). In Fig. 1e we show
four readout traces, which are assigned to ∣⟩↓↓, ∣⟩↑↓, ∣⟩↓↑ and ∣⟩↑↑.
The measured spin readout fidelity is 96.5% ± 1.1% for L and
91.8% ± 1.5% for R, with a total sequential measurement fidelity of
93.9% ± 1.3% (see Supplementary Information section I). The relaxa-
tion time of ∣⟩↑, T 1 , was measured to be 0.48 ± 0.08 s for L and
0.11 ± 0.03 s for R, consistent with previous theoretical and experimen-
tal results^25. We also measure a tunnel coupling of tc/h = 4.3 ± 0.4 GHz,
which we define as half of the energy gap of the S(1,3) and S(2,2) anticross-
ing, by fitting to the so-called ‘spin-funnel’ shown in Fig. 2a–c. This tc
has been engineered to be considerably larger than that of previously
measured devices^19 by combining smaller inter-dot separation and the
presence of the additional electron on the 3P quantum dot (see
Supplementary Information section II).
To demonstrate coherent control over the exchange interaction
required to perform a SWAP gate we first show classical correlations
between the two qubits^17 ,^19. We use the pulse sequence shown in
Fig. 2d, e to investigate the spin correlations between the antiparallel
spin states, ∣⟩↑↓ and ∣⟩↓↑, as a function of detuning. We note that the
electrons are initialized into a mixture of ∣⟩↑↓ and ∣⟩↓↓ in the (1, 3)
charge region because it is not possible to deterministically load ∣⟩↑
electrons. We then apply a voltage pulse ε along the detuning axis to
control the strength of J. To investigate our ability to switch J on and
off, we vary our detuning pulse amplitude towards the (1, 3) ↔ (2, 2)
anticrossing while waiting for 5 ms (much longer than the electron spin
dephasing time, T 2 ∗) and measure the resulting two-spin probabilities
P; see Fig. 2f. At very negative detuning, deep in the (1, 3) charge region,
the electron spins are separate and remain in the initial state,
ρi=↑()∣⟩↓↑⟨∣↓+∣⟩↓↓ ↓↓ /⟨∣ 2 because P↑↓ ≈ P↓↓ ≈ 50%. As the
detuning pulse approaches ε = 0 mV, we observe P↑↓ → 25% and
P↓↑ → 25% as expected, which is an indication of the onset of the
exchange interaction because J causes rotation between these two
states^17. By contrast, P↓↓ and P↑↑ remain in their initial population
because these states are unaffected by the exchange interaction.
We now investigate the temporal control over the exchange by fixing
the detuning position and varying the duration of the exchange pulse
to determine the decay of the oscillations between ∣⟩↑↓ and ∣⟩↓↑. Here
we use the pulse scheme with the corresponding energy level diagram
in Fig. 3a–c. The large amplitude of about 40 mV, combined with the
fast rise time of about 100 ps, creates a near perfect non-adiabatic pulse.
In Fig. 3d we show normalized oscillations in P↑↓ at various detuning
positions with frequency ħΩε=ΔEJZ^2 +(,tc)^2 , which corresponds
to the difference in energy between the T 0 state and the low-lying sin-
glet state in the range 130–580 MHz. We can immediately see the effect
of charge noise on the decay of the oscillations. As J becomes larger, the
oscillations decay more rapidly owing to the larger effective noise in J
because^16 T 2 SWAP∝/ddJ ε. By fitting the oscillations to a quasi-static
charge noise model we estimate the detuning noise in our device, which
is determined to be σε ≈ 16 − 100 μeV at an electron temperature of
330 mK depending on the assumed curvature of J near ε = 0 mV (see
Supplementary Information section III). Because the charge noise is
known to scale with the electron temperature^16 , future work will focus
on reducing the electron temperature of our devices.
Finally, we demonstrate the SWAP gate, where we use the pulse
scheme shown in Fig. 4a, b to generate the input states ρ↓↓=↓∣⟩↓↓⟨∣↓,
ρ↑↓=↑()∣⟩↓↑⟨∣↓+∣⟩↓↓ ↓↓ /⟨∣ 2 , ρ↓↑=↓((∣⟩↑↓⟨∣↑+∣⟩↓↓ ↓↓⟨∣)) 2/^
and ρRR=↑()∣⟩↑↑⟨∣↑+∣⟩↑↓ ↑↓⟨∣+↓∣⟩↑↓⟨∣↑+∣⟩↓↓ ↓↓ /⟨∣ 4 (see
Supplementary Information section IV). For the SWAP gate we use
Ω/2π ≈ 300 MHz because for this value of exchange we achieve an
optimal trade-off between long coherence time (small dJ/dε) and high
visibility oscillations (large J > ΔEZ). For initial states ρ↑↓ and ρ↓↑ we
see oscillations that are π out of phase for P↑↓ and P↓↑ owing to the
exchange interaction. After about 0.8 ns, P↑↓ ≈ P↓↑, demonstrating a
SWAP gate; at about 1.6 ns, P↑↓ and P↓↑ have switched values, show-
ing that a SWAP gate has been achieved. As expected, ∣⟩↓↓ and ∣⟩↑↑13 nm100 nmBMiddle gate B
Right gateSource DrainSET gateLeft gate
L dot R dot↑↓
↓↓
↓↑
↑↑Left-gate voltage (V)Right-gate voltage (V)0.40 0.50 0.600.850.951.054080P↑
P↓EFRead right dot (D^0 )Read left dot (D–)a
c debRF-SET signal (mV)Readout time (ms)0510 15 20 25Right dot(1,3)(2,3)(1,2) (2,2)Left dotSET[110]SET L dotR dot SETSET L dotR dot SETFig. 1 | High-fidelity, independent single-shot spin readout of two
donor qubits. a, STM micrograph of the two-qubit device. The lighter
regions show the open lithographic hydrogen mask. The device consists^
of four gates: left, middle, right and the SET gate used to control the
electrochemical potentials of the qubits and the RF-SET. b, Close-up STM
micrograph of the RF-SET and the two donor dots that define the qubits L
(left) and R (right). The donor quantum dots (L, 2P; R, 3P) are separated
by 13.0 ± 0.5 nm. c, Reflected amplitude of the RF-SET as a function of the
left- and right-gate voltages with electron numbers (nL, nR). The white
lines indicate charge transitions between individual qubits and the RF-SET.
The blue and red dots mark the position where spin readout is performed
on the left and right qubit, respectively. d, Electrochemical potentials μ↑
and μ↓ of the two qubits (with spin ∣⟩↑ and ∣⟩↓, respectively), showing
how the electron spin states are measured using an energy-selective
protocol. For R we use the standard D^0 -style readout and for L we use a
D−-style readout^24 , which involves conditionally loading an electron onto
the quantum dot. e, Reflected RF-SET amplitude measured as a function of
time, used to distinguish between the four possible qubit states. The rising
(falling) edge of events in the readout trace corresponds to ∣⟩↑ ()∣⟩↓
electron tunnelling to (from) the RF-SET.
372 | NAtUre | VOL 571 | 18 JULY 2019