Single-Shot Readout of Multiple Donor Electron Spins with a Gate-Based Sensor

Proposals for large-scale semiconductor spin-based quantum computers require high-fidelity single-shot qubit readout to perform error correction and read out qubit registers at the end of a computation. However, as devices scale to larger qubit numbers integrating readout sensors into densely packed qubit chips is a critical challenge. Two promising approaches are minimizing the footprint of the sensors, and extending the range of each sensor to read more qubits. Here we show high-fidelity single-shot electron spin readout using a nanoscale single-lead quantum dot (SLQD) sensor that is both compact and capable of reading multiple qubits. Our gate-based SLQD sensor is deployed in an all-epitaxial silicon donor spin-qubit device, and we demonstrate single-shot readout of three ${}^{31}\mathrm{P}$ donor quantum dot electron spins with a maximum fidelity of 95%. Importantly, in our device the quantum dot confinement potentials are provided inherently by the donors, removing the need for additional metallic confinement gates and resulting in strong capacitive interactions between sensor and donor quantum dots. Our results are consistent with a $1/d^{1.4}$ scaling of the capacitive coupling between sensor and ${}^{31}\mathrm{P}$ dots (where $d$ is the sensor-dot distance), compared to $1/d^{2.5-3.0}$ in gate-defined quantum dot devices. Due to the small qubit size and strong capacitive interactions in all-epitaxial donor devices, we estimate a single sensor can achieve single-shot readout of approximately 15 qubits in a linear array, compared to 3–4 qubits for a similar sensor in a gate-defined quantum dot device. Our results highlight the potential for spin-qubit devices with significantly reduced sensor densities.

Popular Summary

Semiconductor spin-qubit devices are promising candidates for large-scale quantum computers, as they use materials and nanofabrication processes that have been extremely well developed over several decades by the computer chip industry. The nanoscale size of semiconductor quantum bits (or qubits) is promising for packing the millions of qubits that will eventually be required onto a compact chip. However, such small qubit sizes pose a dual challenge, as the circuitry required for qubit control and readout must also be nanoscopic and packed densely on the chip to make a fully functioning quantum processor.

To save space on the qubit chip, recent advances have developed multipurpose gate electrodes, for which the same physical gate is used for both qubit control and readout (called gate-based sensors). By developing hardware components with multiple functionalities, excess control components can be eliminated and valuable chip space saved. However, to date the qubit readout functionality of gate-based sensors has been limited to reading only a single qubit per sensor.

In our work, we engineer an atomic scale, gate-based sensor that is capable of reading out significantly more than one qubit. We demonstrate readout of three qubits with fidelities of up to 95%, and show that is feasible to read 15 qubits with our present sensor, in contrast to 3–4 qubits for alternative approaches with similar sensor performance. Our work highlights a promising pathway for qubit readout in semiconductor quantum processors, with compact sensors that can potentially be reduced in on-chip density by an order of magnitude.

Figure 1

Donor-based quantum dot device with integrated SLQD charge sensors. (a) STM image of the device and gate labels. SLQD1 is used to sense the donor quantum dots ($D1$, $D2$, $D3$, and $D4$). Based on STM images and electrically measured charging energies, we estimate the number of ${}^{31}\mathrm{P}$ donors in each to be two for $D1$, three for $D2$, three for $D3$, and one for $D4$. Electrons are loaded onto the donors from $R1$ ($D1$, $D2$) or $R2$ ($D3$, $D4$) and onto SLQD1 from $L1$. A second SLQD (SLQD2) is not used in our experiments. (b) Schematic of SLQD charge-sensor operating principle. A quantum dot (SLQD1) tunnel coupled to an electron reservoir ($L1$) is embedded in a resonant circuit formed by a $\mathrm{Nb}\mathrm{Ti}\mathrm{N}$ superconducting spiral inductor, measured using standard reflectometry techniques [7]. When an ac excitation is applied to $L1$, cyclical single-electron tunneling generates quantum capacitance in the circuit when the Fermi energy in $L1$ is aligned with an available charge state of SLQD1. A change in the electrostatic environment causes the resulting Coulomb-like peaks to shift, allowing operation as a charge sensor. (c) Charge-stability diagram for $D1$ and $D2$ sweeping $V_{L1}$ and $V_{R1}$. The periodic diagonal lines in the data are SLQD1 transition lines, with donor charge transitions from $D1$ and $D2$ being observed as breaks in the SLQD lines (example break shown in inset). The overlaid white dashed lines indicate $D1$ charge transitions and the red dashed lines indicate $D2$ charge transitions. (d) Charge-stability diagram for $D3$ and $D4$ sweeping $V_{L1}$ and $V_{R2}$. The red dashed lines now indicate $D3$ charge transitions, and the white dashed lines $D4$ charge transitions. We note that here the $D3$ and $D4$ transition line slopes are similar; we identify the charge transitions by sweeping other gate combinations.

Figure 2

Single-shot electron spin readout on $D1$, $D2$, and $D3$ donor quantum dots. (a) Gate-gate map showing break in SLQD1 transition line when the first electron is loaded onto $D1$. The approximate pulse positions for the readout sequence are indicated by the white stars. The read level is calibrated so that a spin-up electron can tunnel from $D1$ to $R1$, but a spin-down cannot. (b) Example single-shot readout traces showing spin-up and spin-down signals. Due to the fast tunnel rate at this transition, some of the rapid spin-up traces are not registered, leading to an average fidelity of 81%. (c) Similar gate-gate map for $D2$. Readout for $D2$ is performed at the second electron transition via the $D^{-}$ charge state [29]. Here we choose the read position on the opposite side of the SLQD charge break to make spin up the high sensor level for consistency with $D1$ and $D3$. (d) Example single-shot readout traces for $D2$. (e) Gate-gate map for $D3$. (f) Example single-shot readout traces for $D3$. (g) Gate-gate map for $D4$. For this donor quantum dot, the tunnel rate between the donor and reservoir is too fast to perform single-shot spin readout. In fact, a faint signal can be observed due to cyclical driving of an electron between the $D4$ and $R2$. This implies that the tunnel rate is non-negligible compared to the rf reflectrometry frequency (130 MHz). (h) Enlargement of the region from (g), highlighting the dispersive signal generated by cyclical tunneling of the $D4$ electron.

Figure 3

Importance of the sensor shift $V_M$ for long-range qubit readout. (a) comsol simulation of $V_M$ for our device geometry. The dashed contour line indicates the estimated strong response regime boundary. (b) Fit to comsol simulated $V_M$ values as a function of distance $d$ from SLQD1. The simulated values (blue dots) follow a $1/d^{1.4\pm 0.1}$ dependence (orange line), which match the experimental values (red circles). The yellow line is a $1/d^3$ fit (as observed in planar gate-defined devices) to the experimental data, which is inconsistent with both the simulated and measured values. (c) Comparison of readout contrast possible for 100-, 200-, and 300-nm sensor-qubit distance for $1/d^{1.4}$ scaling (left panel) and $1/d^3$ scaling (right panel). At 300 nm, the sensor peaks for the two readout charge states are almost overlapping in the $1/d^3$ case, whereas significant discrimination is still possible for $1/d^{1.4}$. (d) Estimated single-shot readout fidelity as a function of qubit distance to SLQD1. The input parameters to the fidelity calculation (tunnel rates, $T_1$ relaxation time, noise level) are taken from the experimentally measured values for $D3$. The blue curve is for $1/d^{1.4\pm 0.1}$, with the shaded region outlining the uncertainty bounds from the fit in Fig. 3. The orange curve is for $1/d^3$, and exhibits a much faster roll-off in readout fidelity. Over 90% fidelity is possible out to 300 nm for $1/d^{1.4}$, compared to 130 nm for $1/d^3$.