High-Fidelity Single-Shot Readout for a Spin Qubit via an Enhanced Latching Mechanism

The readout of semiconductor spin qubits based on spin blockade is fast but suffers from a small charge signal. Previous work suggested large benefits from additional charge mapping processes; however, uncertainties remain about the underlying mechanisms and achievable fidelity. In this work, we study the single-shot fidelity and limiting mechanisms for two variations of an enhanced latching readout. We achieve average single-shot readout fidelities greater than 99.3% and 99.86% for the conventional and enhanced readout, respectively, the latter being the highest to date for spin blockade. The signal amplitude is enhanced to a full one-electron signal while preserving the readout speed. Furthermore, layout constraints are relaxed because the charge sensor signal is no longer dependent on being aligned with the conventional (2,0)–(1,1) charge dipole. Silicon donor-quantum-dot qubits are used for this study, for which the dipole insensitivity substantially relaxes donor placement requirements. One of the readout variations also benefits from a parametric lifetime enhancement by replacing the spin-relaxation process with a charge-metastable one. This provides opportunities to further increase the fidelity. The relaxation mechanisms in the different regimes are investigated. This work demonstrates a readout that is fast, has a one-electron signal, and results in higher fidelity. It further predicts that going beyond 99.9% fidelity in a few microseconds of measurement time is within reach.

Popular Summary

Quantum computers promise to solve certain problems much more efficiently than their classical counterparts. Electron spins can be employed to store quantum bits (qubits) in electronic chips that are similar to microprocessors. However, qubits are more prone to errors than transistors. Improvements in measurement fidelity, therefore, are greatly desirable. In this work, we experimentally and theoretically study a measurement scheme that reduces these errors to close to 1 in 1000—the lowest to date for spin qubits.

Our measurement technique exploits spin-to-charge mapping processes, which generate signals that are larger and longer lasting than the conventional “spin blockade” approach. Despite the additional measurement steps, these improvements reduce the error rates and improve the speed.

Previous work suggested that additional charge mapping processes could lead to large benefits; however, uncertainties remained about the underlying mechanisms and achievable error rates. Our work convincingly demonstrates the advantages of this new measurement scheme and identifies various mechanisms that play a crucial role in its successful implementation.

Our measurement combines the strengths of other established methods that achieved either speed or large signal separately, and it is applicable to a large class of spin-based quantum computers.

Figure 1

(a) Scanning electron microscope image of the gate structure used to define the QD and CS. The blue overlay indicates the approximate shape of the electron gas. The QD is pushed to the right side and tunnel coupled to a single reservoir. Phosphorus donors have been implanted in a self-aligned way at the location indicated by the red dot. Some donors are tunnel coupled to the QD. Gates CP and AG are used to control the effective double QD through voltages $V_{\mathrm{CP}}$ and $V_{\mathrm{AG}}$. (b) MOS device gate stack along the dashed line of panel (a). (c) The QD-D system effectively forms a double-QD-like system where D states have 0 or 1 electron and little or no coupling to a charge reservoir. (d) Charge anticrossing between a QD and a D state. The absence of reservoir for the D makes the charge states latch, which is made apparent by reversing the sweep direction of the scan. The dashed lines indicate where the equilibrium $\mathrm{D}\leftrightarrow \mathrm{lead}$ transition should be. Color scale: $d{I}_{\mathrm{CS}}/d{V}_{\mathrm{CP}}$ (a.u.).

Figure 2

(a,b) Two variations of the ELR. In a typical experiment, one would control a ST qubit at point A and pulse to point P in the PSB region for PSB readout (PSBR). From there, an additional pulse to point M for measurement allows the selective mapping of one of the PSB states to a different charge occupation, therefore enhancing the amplitude of the sensed charge signal. Because the $\mathrm{D}\leftrightarrow \mathrm{lead}$ tunnel rate is very small, the corresponding line in the charge-stability diagram can be ignored. The thicker black lines represent relatively fast transitions. A nice way to understand the cause of the enhancement is that the excited state in the PSB region sees a shifted anticrossing; therefore, it does not cross the same $\mathrm{QD}\leftrightarrow \mathrm{lead}$ transition lines as the ground state does when going from point P to point M. (c,d) Energy levels and state ladder at point M. The $(1,1)S$ [or $(1,1)\uparrow \downarrow$] is mapped to $(2,0)S$ through rapid (or slow) adiabatic passage from A to P. From P to M, tunneling processes with the lead perform the enhancement. The $\epsilon$ and $\delta$ parameters can be used to follow the energy detunings throughout the sequence. See Sec. 2b3 for details. (e,f) A pulse sequence where the M point is swept, used to image the edges of the PSB and enhancement regions of donor 1. The measurement is initialized with a random state and averaged over many cycles. Color scale: $d{I}_{\mathrm{CS}}/d{V}_{\mathrm{CP}}$ (a.u.).

Figure 3

(a)–(d) Relaxation or excitation time versus the detuning $\epsilon$ for the different readouts on donor 1. The data are taken along detuning cuts schematized in panel (a). Non-negligible excitation times are only observed in the PSBR case. For the ELR, excitation is strongly suppressed by the large $\delta >100\mu \mathrm{eV}$ energy cost (see Fig. 2). The fit in panel (b) corresponds to a simple relaxation model where the metastable relaxation rate ${\mathit{\Gamma }}_{\mathrm{MS}}={\mathit{\Gamma }}_{(2,1)\leftarrow (1,1)}{\beta }^2$ and $\beta \approx t_C/\epsilon$ from the interdot tunnel coupling $t_C$ (full gap). Here, $\epsilon$ is calibrated with the measured lever arm parallel to the $\mathrm{QD}\leftrightarrow \mathrm{lead}$ transition ($32.4\mu \mathrm{eV}/\mathrm{mV}$), and the QD loading rate ${\mathit{\Gamma }}_{(2,1)\leftarrow (1,1)}=2.56\mathrm{MHz}$ is measured independently. The fit yields $t_C=0.54\mu \mathrm{eV}$. This value is consistent with independent measurements through diabatic or adiabatic passage experiments.

Figure 4

(a) Anticrossing of donor 2 (no pulse applied) and pulse sequence used to demonstrate the high-fidelity direct ELR. Color scale: $d{I}_{\mathrm{CS}}/d{V}_{\mathrm{CP}}$ (a.u.). (b) This QD-D anti-crossing can produce low-visibility hyperfine-driven coherent rotations as in Ref. [21]. The visibility is limited by the low bandwidth of the pulse compared with the $t_C$ and effective magnetic field difference $\mathrm{\Delta }{B}_z$. (c) An averaged measurement technique, which is used to image the edges of the enhancement region by varying the location of the measurement point.

Figure 5

(a,b) Single-shot time traces for the PSB readout and ELR of donor 2. The enhancement in signal is clearly visible for the ELR case. (c,d) Probability density of finding a certain CS current after the signal is stabilized for a $10\text{−}\mu \mathrm{s}$ time bin. It shows the enhancement in signal, while the noise magnitude stays the same and is well modeled by a Gaussian fit with standard deviation 26.8 pA. (e) The error probability ${\overline{e}}_{\mathrm{meas}}$, which first decreases as the readout duration is increased because of the reduced effect of noise in the state estimation. If the duration is too long, errors from the relaxation or excitation become the dominant source. The ELR shows a factor of 8 enhancement in charge measurement error, 2.3 reduction in measurement time, and 3.7 improvement in signal. The limiting factor to the detection time is the limited bandwidth of the system, which introduces a significant rise time to the signal, despite the large signal-to-noise ratio of the ELR for $10\text{−}\mu \mathrm{s}$ time bins. This suggests that large improvements are still possible.