Noise-protected two-qubit gate using anisotropic exchange interaction

Abstract

Hole spin qubits hosted in Germanium quantum dots are promising candidates for scalable quantum computing. The strong spin-orbit interaction can enable fast and all-electrical quantum control. Furthermore, the platform can implement universal quantum control using only baseband signals, which may mitigate the impact of crosstalk and microwave-induced heating. At the same time, spin-orbit interaction gives rise to an anisotropic exchange interaction, whose potential for implementing two-qubit gates has remained largely unexplored. However, the current performance of operating a hole-based quantum computer is mostly limited by dephasing due to low-frequency charge noise. In this work, we propose a novel two-qubit gate protocol for Germanium hole spin qubits operated in the gapless regime. This gate protocol exploits the anisotropic exchange interaction between neighboring spins and utilizes a composite pulse scheme implemented solely through electrical baseband signals. Using this approach, we predict high-fidelity two-qubit controlled-Z operations that can suppress exchange-energy fluctuations, offering a pathway toward fault-tolerant semiconductor quantum processors.

Figures (9)

• Figure 1: (a) Simulated average gate fidelities (Eq. \ref{['Average gate fidelity']}) of a single-pulse X gate (top) and a SCROFULOUS composite-pulse X gate (bottom) in the presence of pulse length errors. (b) Bloch-sphere trajectories for a single-pulse (top) and a SCROFULOUS composite-pulse (bottom) $R_y(\pi/2)$ gate. Each individual rotation is assumed to experience a $10\%$ under-rotation error. Starting from the $|0\rangle$ state (pointing along $+z$), the final state after the single-pulse gate deviates significantly from the target position along the $+x$ direction, whereas the SCROFULOUS gate brings the state much closer to the target. (c) Illustration of isotropic and anisotropic exchange interactions between spins in adjacent quantum dots. The isotropic exchange is described by $H = J_0\,\vec{S}_1 \cdot \vec{S}_2$, whereas the anisotropic exchange takes the form $H = J_0\,\vec{S}_1 \cdot (R\,\vec{S}_2)$, with $R$ a rotation matrix.
• Figure 2: Schematic of the device architecture used in the operating scheme. Qubit 1 is tuned by pulsing the central gate voltage such that $g_{xx} = -g_{yy}$, while qubit 2 is squeezed along the $y$-direction resulting in $g_{yy} = 0$. The green regions represent the spatial extension of the two qubits’ wavefunctions, whose overlap gives rise to the exchange interaction.
• Figure 3: (a) Average gate fidelity comparison between the SCROFULOUS gate and a single-pulse $e^{-i\frac{\pi}{4}\sigma_z \sigma_z}$ gate realized by two Ge hole spin qubits in the presence of $\mathcal{J}$-tensor fractional error $\epsilon$. (b) Logarithmic scale magnification of the small-error region displayed in panel (a). The single-pulse ZZ$_{\pi/4}$ gate slightly outperforms the SCROFULOUS gate for extremely small $|\epsilon|$, but its fidelity decreases rapidly as $|\epsilon|$ increases.
• Figure 4: Comparison of gate fidelities in the presence of voltage noise affecting both the g-tensors and the exchange coupling. The fidelities are calculated using a Monte Carlo simulation, based on the details provided in Appendix \ref{['Appendix C']}. (a) Gate-fidelity density plot for the SCROFULOUS gate. (b) Gate-fidelity density plot for the single-pulse ZZ gate. (c) Difference in logarithmic gate infidelity between the two protocols, defined as $\ln(1 - F_{\text{Single}}) - \ln(1 - F_{\text{SCROFULOUS}})$ and evaluated at identical $\sigma_{\delta V}$ and $\alpha$. Positive values correspond to parameter regimes in which the SCROFULOUS gate outperforms the single-pulse ZZ gate.
• Figure 5: (a) Voltage pulse with two additive ramp segments of duration $T$. The total duration of the pulse sequence is $t_1 + t_2 + t_3 + 2T$. (b) Voltage pulse with embedded ramp time $T$, where the two ramps are incorporated into the three SCROFULOUS gate segments $t_1$, $t_2$, and $t_3$. The total duration remains $t_1 + t_2 + t_3$ and the pulse takes a symmetric shape. The durations $t_1$, $t_2$, and $t_3$ are specified in Appendix \ref{['Appendix C']}. (c) Average gate fidelity as a function of the ramp time $T$ for the two ramping protocols shown in (a) and (b): pulse with additive ramps (blue) and embedded ramps (red). The embedded-ramp pulse exhibits a significant enhancement in gate fidelity, without showing rapid oscillations. (d) Average gate fidelity comparison between the original embedded-ramp pulse and the optimized pulse.