Harnessing electron motion for global spin qubit control

TL;DR

This work tackles the challenge of scaling microwave control for silicon spin qubits by introducing motion-based g-factor homogenisation, enabling global control with a single drive. It presents two physically distinct routes—exchange-based homogenisation and spin shuttling—demonstrating through numerical simulations that qubit frequencies can be effectively averaged to enable high-fidelity single-qubit operations and extend to two-qubit gates. The study analyzes concrete architectures, including a 2×N quantum-dot array and a looped pipeline, showing up to two orders of magnitude fidelity improvement over Stark-shift-based approaches in favorable dispersion regimes and providing a pathway for scalable, low-complexity quantum control. These results suggest a practical route toward fault-tolerant silicon-qubit processors by reducing microwave hardware requirements and enabling global gate schemes, with clear directions for handling noise, other qubit platforms, and advanced device topologies.

Abstract

Silicon spin qubits are promising candidates for building scalable quantum computers due to their nanometre scale features. However, delivering microwave control signals locally to each qubit poses a challenge and instead methods that utilise global control fields have been proposed. These require tuning the frequency of selected qubits into resonance with a global field while detuning the rest to avoid crosstalk. Common frequency tuning methods, such as electric-field-induced Stark shift, are insufficient to cover the frequency variability across large arrays of qubits. Here, we argue that electron motion, and especially the recently demonstrated high-fidelity shuttling, can be leveraged to enhance frequency tunability. Our conclusions are supported by numerical simulations proving its efficiency on concrete architectures such as a 2$\times$N array of qubits and the recently introduced looped pipeline architecture. Specifically, we show that the use of our schemes enables single-qubit fidelity improvements up to a factor of 100 compared to the state-of-the-art. Finally, we show that our scheme can naturally be extended to perform two-qubit gates globally.

Figures (16)

• Figure 1: Schematic time-evolution of a single qubit oscillating between two quantum dots with distinct frequencies $\omega_{q,1}$ (red) and $\omega_{q,2}$ (yellow). We assume that the transfer rate between the dots is fast enough that the electron instantaneously swaps position after each time step. Assuming that it starts in the first dot, the qubit rotates by one tile and ends up in the second dot after one time step. Next, it rotates by three tiles and comes back to the first dot. Finally at $t=4dt$, the qubit is back to its original position and has covered eight tiles. This leads to the conclusion that the resulting dynamics is a precession of the qubit at a frequency $\bar{\omega}_q = (\omega_{q,1}+\omega_{q,2})/2$.
• Figure 2: Physical implementations of the motion-based $g$-factor homogenisation. In (a), we consider two quantum dots with respective $g$-factors $g_1$ and $g_2$. The exchange coupling $J$ is used to homogenise the frequencies of the two electrons. This allows to reduce the number of distinct frequencies in the spectrum and thus reduce crosstalk. In (b) we use a completely different method in which we physically move the electron to perform the homogenisation. Here, the $g$-factor evolves continuously along the shuttling path. We find that this method is the most powerful as it can be generalised to an arbitrary number of qubits and scales better.
• Figure 3: Time evolution of $\langle\sigma_z\otimes I\rangle$ and $\langle I\otimes\sigma_z\rangle$ under the two-qubit Hamiltonian of \ref{['eq:hamiltonian']}. We set $\omega_q^{12}=\Omega$ and $J=20 \, \omega_q^{12}$ where $\omega_q^{12} = (\omega_{q,2}-\omega_{q,1})$. The initial state is given in \ref{['eq:init_state_swap']}. The faded lines correspond to the full time evolution, while the solid lines are obtained from sampling the full data every $2\pi/J$.
• Figure 4: Infidelity of the swapping protocol. It is computed as the infidelity of implementing an $X\otimes X$ gate when driving two continuously-swapped qubits with frequencies $\omega_{q,1}$ and $\omega_{q,2}$ with a single driving tone at $\omega=\bar{\omega}_q$. The data is plotted against $J/\Omega$ and $\omega_q^{12}/\Omega$, where $J$ is the exchange coupling and $\omega_q^{12}=\omega_{q,2}-\omega_{q,1}$. $J$ is always chosen such that the condition in \ref{['eq:integer_J']} is satisfied.
• Figure 5: Illustration of the impact of speed and explored distance on the quality of the homogenisation process. The $x$-axis represents the difference between the electron's homogenised frequency $\bar{\omega}_d$ when shuttled for a distance $d$ and the device-averaged one $\omega_0 = g_0B_0$. (a) Wide distribution around the mean frequency representing an imperfect homogenisation. (b) Increasing the speed (i.e. the transfer rate) while keeping the explored distance fixed improves the quality of the homogenisation as explained before. This is represented by a more peaked Gaussian centred around $\bar{\omega}_d$, which is reminiscent of the frequency narrowing phenomenon. The faded Gaussian is plotted for comparison. (c) Increasing the shuttled distance while keeping the same speed deteriorates the homogenisation as the electron explores more dots. The shift of the mean frequency manifests the fact that $\bar{\omega}_{d}\rightarrow \omega_0$ as $d\rightarrow\infty$.