Single-Shot Spin Readout in Semiconductors Near the Shot-Noise Sensitivity Limit

Fault-tolerant quantum computation requires qubit measurements to be both high fidelity and fast to ensure that idling qubits do not generate more errors during the measurement of ancilla qubits than can be corrected. Towards this goal, we demonstrate single-shot readout of semiconductor spin qubits with 97% fidelity in $1.5\mu \mathrm{s}$. In particular, we show that we can engineer donor-based single-electron transistors (SETs) in silicon with atomic precision to measure single spins much faster than the spin decoherence times in isotopically purified silicon ($270\mu \mathrm{s}$). By designing the SET to have a large capacitive coupling between the SET and target charge, we can optimally operate in the “strong-response” regime to ensure maximal signal contrast. We demonstrate single-charge detection with a signal-to-noise ratio (SNR) of 12.7 at 10 MHz bandwidth, corresponding to a SET charge sensitivity (integration time for $\mathrm{SNR}=2$) of 2.5 ns. We present a theory of the shot-noise sensitivity limit for the strong-response regime which predicts that the present sensitivity is about one order of magnitude above the shot-noise limit. By reducing cold amplification noise to reach the shot-noise limit, it should be theoretically possible to achieve high-fidelity, single-shot readout of an electron spin in silicon with a total readout time of approximately 36 ns.

Popular Summary

To create a practical quantum computer, it is essential to correct the errors that naturally occur during each step of the computation. To achieve this, researchers require the ability to read out the state of the quantum bits (qubits) accurately and quickly. The speed at which the qubit state is read out must be much faster than the rate at which information on the qubits is lost. By engineering highly sensitive detectors at the nanoscale, we have reached a new “strong-response” regime, allowing us to read out the qubit state in microseconds compared to milliseconds while retaining high accuracy, a 2-orders-of-magnitude improvement over previous results.

The small size of our detector allows us to switch from “fully on” to “fully off” states which, coupled with our ability to position the qubit and detector with atomic-level precision, allows for strong interactions and a high signal-to-noise ratio. In contrast to previous detectors that focused on detecting small shifts in the signal, this new strong-response regime distinguishes the discrete states of our single-electron qubits. This allows us to read out a single electron spin on phosphorus-atom qubits in silicon in just $1.5\mu \mathrm{s}$. Theoretical analysis shows that we are within one order of magnitude of the shot-noise limit, where, with straightforward technical improvements, we anticipate further improvements in readout times down to about 400 ns.

These results open the door to realistic error correction in silicon-based quantum computation.

Figure 1

Strong response of a donor-based rf SET. (a) STM image of the device with external reflectometry circuit schematic. Lighter patches are regions where the passivating H layer has been removed ready for P incorporation to create in-plane conducting gates ($G1$, $G2$, GT, and GSET), SET charge detector (SET, $S$, and $D$), and donor quantum dots ($D1$ and $D2$). A radio-frequency carrier wave is attenuated down to the 60 mK stage where it is reflected by the resonant $LC$ tank circuit, amplified at 4 K and room temperature, and then demodulated into $I$ and $Q$ components. (b) Charge stability diagram showing the rf SET response as a function of gate voltages $V_{\mathrm{GT}}$ and $V_{G12}$ (linear combination of $V_{G1}$ and $V_{G2}$) at an electron transition on $D1$. (c) The contrast in rf response ($\delta R$, $\mathrm{\Delta }R$) of the SET as a function of the chemical potential $\mu$ in the weak-response (upper) and strong-response (lower) regimes, respectively, in terms of the SET charging energy $E_C$. The rf response reaches $R_{\min }$ during Coulomb blockade and $R_{\max }$ atop a Coulomb peak and shifts by the mutual charging energy ($\delta \mu$, $\mathrm{\Delta }\mu$) in the respective weak-response and strong-response regimes due to a single-electron transition. The SET signal can switch between $R_0$ (lower black dot) and $R_1$ (upper black dot) for a given chemical potential.

Figure 2

High-sensitivity charge detection. (a) Examples of charge transition events of the third electron on the right donor dot ($D2$) detected by the change in rf SET response. (b) 2D histogram in $I\text{−}Q$ space showing the bimodal Gaussian distribution of many charge detection traces of the third electron on $D2$ measured with $-85\mathrm{dBm}$ rf power reaching the device. The distribution shows two clear peaks centered around $R_0$ and $R_1$ (separated by ${\mathrm{\Delta }}_{\mathrm{rf}}$) with standard deviations of noise ${\sigma }_0$ and ${\sigma }_1$ corresponding to the respective ON and OFF electron charge states on the donor quantum dot. (c) The theoretically optimal sensitivity, characterized by the measurement time ${\tau }_m$, as a function of the rms rf current through the rf SET. The black dashed line indicates the theoretical shot-noise limit. Solid curves show how ${\tau }_m$ increases with additional amplifier noise, with noise temperature between 0.3 and 30 K. A star indicates approximately the sensitivity achieved in the present experiment.

Figure 3

$\mu \mathrm{s}$ electron spin readout. (a) Single-shot spin readout is performed in a global magnetic field $B=1.5\mathrm{T}$ by pulsing gate voltages to read spin states via energy selective tunneling. Each readout trace is declared spin-up or -down, respectively, if the detector response rises above a set threshold (blue, spin-up) or not (red, spin-down) during the optimal readout time $\mathrm{\Delta }{t}_{\mathrm{opt}}=1.5\mu \mathrm{s}$. Traces are offset for clarity with pairs of dotted lines depicting $R_0$ and $R_1$. (b) The readout time $\mathrm{\Delta }t$ is varied to optimize state fidelities ($F^{\uparrow }$ and $F^{\downarrow }$ for $|\uparrow ⟩$ and $|\downarrow ⟩$, respectively) and visibility ($V$) and is optimal at $1.5\mu \mathrm{s}$, where $V=97.8\%$. (c) Increasing the rf-input power increases $T_e$ above 200 mK. When scaled to absolute applied power, heating due to dc current (black dots) and rf-input power (red dots) shows the same trend. Black dotted lines mark the optimal powers used for charge detection ($-85\mathrm{dBm}$) and spin readout ($-97\mathrm{dBm}$).

Figure 4

rf SET matching circuit schematic. We represent the SET by conductance $G_{\mathrm{SET}}$, which is connected to a transmission line of characteristic impedance $Z_0$ via an $L$-match filter circuit consisting of inductance $L_0$, capacitance $C_0$, and parasitic dissipation represented by conductance $G_0$. The current source at right represents the shot-noise contribution of the SET, $I_{\mathrm{SHOT}}$.

Figure 5

Characterization of the resonator circuit. Panels (a) and (b) show the rf amplitude $|V_{\mathrm{OUT}}|$ and phase, respectively, as a function of the rf-input frequency used showing a clear resonance around 223 MHz. The resonance changes significantly between cases in (black) and out (red) of Coulomb blockade. (c) Internal (empty circles) and external (filled circles) quality factors as a function of gate voltage across a Coulomb peak. The external quality factor is constant while the internal quality factor changes by a factor of 4. Dotted lines show when internal and external quality factors are approximately equal, corresponding to the impedance matching condition. (d) Rising (blue) and falling (red) response of the resonating circuit as it is pulsed in and out of Coulomb blockade by a 50 kHz square pulse on a nearby electrical control gate. The responses are fitted to exponential decays (black dash) to extract a rise time $T_{\text{rise}}=42.7\mathrm{ns}$ and fall time $T_{\text{fall}}=50.8\mathrm{ns}$, reflecting the change in $Q$.

Figure 6

Measured noise levels. (a) dc conductance of the SET as a function of dc bias $V_S$ and gate voltage $V_{G1}$ showing the Coulomb diamond structure. (b) Simultaneously measured power spectral density output from the rf measurement chain at 222.3 MHz as a function of $V_S$ and $V_{G1}$. At low bias, noise from the preamplifier dominates and is modulated by the conductance of the SET. At high bias, the noise level is linear with the current in the SET, consistent with SET shot noise. (c) dc current through the SET as a function of $V_S$ at the black dashed line in (a) and (b) ($V_{G1}=0.225\mathrm{V}$). (d) Measured noise output at the dashed line in (b), scaled to an equivalent noise temperature referred to the input of the preamplifier (black). The estimated shot-noise contribution to this noise is plotted as the red curve.

Figure 7

$I\text{−}Q$ histogram of the maximum readout traces’ responses. A 2D histogram of the maximum response of 10 000 readout traces was constructed in $I\text{−}Q$ space. The areas within the two white, dotted circles centered around $R_0$ and $R_1$ depict the distributions of the entire traces that the maximum signals had been sampled from. The histogram shows two distinct distributions corresponding to spin-up and -down that can be separated by a perpendicular threshold 7.4 mV from $R_0$ to distinguish the spin states during electrical readout.

Figure 8

Electrical readout fidelity. The complement of the electrical fidelities $F_{\mathrm{STC}}^{\uparrow }$ (blue) and $F_{\mathrm{STC}}^{\downarrow }$ (red) are shown as a function of the threshold used to distinguish between the two spin states. Reduction in fidelity is either caused by electrical noise or missing very fast tunnel events due to filtering or the limitation of the resonating circuit response time. The optimal threshold in terms of the visibility $V_{\mathrm{STC}}=F_{\mathrm{STC}}^{\uparrow }+F_{\mathrm{STC}}^{\downarrow }-1$ is found to be 7.4 mV from $R_0$ resulting in $V=96.1\%$.