Coherence Protection for Mobile Spin Qubits in Silicon

TL;DR

The paper tackles spin coherence during transport in mobile silicon spin qubits and maps how spatial and temporal noise affects coherence. It introduces a quartet of mitigation strategies—passive gradient reduction, motional narrowing via shuttling, dynamical decoupling during transport, and continuous dressed-state driving—underpinned by a noise-landscape mapping and a Floquet/LZSM framework to model periodic shuttling. Key findings include doubling of stationary dephasing times, extended coherence up to tens of microseconds with shuttling and DD, and further protection with continuous driving yielding $T_R^{\text{sh}}$ values around $20$–$32\ \mu\text{s}$. The work demonstrates that mobile spin qubits can preserve quantum information across transport tasks, significantly relaxing timing constraints for fault-tolerant operations and enabling scalable silicon quantum processors.

Abstract

Mobile spin qubit architectures promise flexible connectivity for efficient quantum error correction and relaxed device layout constraints, but their viability rests on preserving spin coherence during transport. While shuttling transforms spatial disorder into time-dependent noise, its net impact on spin coherence remains an open question. Here we demonstrate systematic noise mitigation during spin shuttling in a linear $^{28}$Si/SiGe quantum dot device. First, by passively reducing magnetic field gradients, we minimize charge-noise coupling to the spin and double the spatially averaged dephasing time $T_2^*(x_n)$ from $4.4$ to $8.5\,μ\text{s}$. Next, we exploit motional narrowing by periodically shuttling the qubit, achieving a further enhancement in coherence time up to $T_{2}^{*,sh} = 11.5\,μ\text{s}$. Finally, we incorporate dynamical decoupling techniques while periodically shuttling over distances exceeding $200\,\text{nm}$, reaching $T_\text{2}^{H,sh}= 32\,μ\text{s}$. For the same setup, we demonstrate that dressed-state shuttling provides robust protection against low-frequency noise with a decay time $T_R^{\text{sh}} = 21\,μ\text{s}$, without the overhead of pulsed control and allowing protection during one-way spin transport. By preserving coherence over timescales exceeding typical gate and readout operations, the demonstrated strategies establish mobile spin qubits as a viable solution for scalable silicon quantum processors.

Figures (22)

• Figure 1: Schematic of the experimental setup and protocol using a mobile electron spin as a quantum sensor. (a) Top-view false-colored scanning electron microscope image of a Si/SiGe device nominally identical to the one used, showing the linear quantum dot array (static dots 1 and 2 are indicated), plunger gates (P1-P6), barrier gates (B0-B6), and sensing dots (SD1, SD2) and a cobalt micromagnet (gray). An external magnetic field $B_{\text{ext}}$ is indicated. (b) Cross-sectional transmission electron microscope image showing the gate stack and $^{28}$Si/SiGe heterostructure. The same false colors are used as in panel (a) for each gate layer, except that here, the gray material on top of the metallization layers is a Pt cap added for improved imaging instead of the micromagnet. A schematic of the potential landscape shows the start and end positions (white dotted lines) of the conveyor transporting qubit 2. Quantum dot 1 is static and contains three electrons, where the one unpaired spin acts as a reference for readout. (c-f) Conceptual overview of strategies to mitigate spin decoherence during shuttling. (c) Passive stabilization: Reducing the longitudinal magnetic field gradient decreases the coupling of charge/electrical noise to the qubit frequency. (d) Motional narrowing: Rapid shuttling boosts spin coherence by averaging out spatially varying noise $\delta B_z (x,t)$, effectively modifying the noise power spectral density seen by the qubit. (e) Dynamical decoupling (DD): Periodic shuttling is combined with DD pulses ($\pi_x$) applied during the stationary intervals between transport segments. (f) Dressed-state shuttling: Continuous driving ($\Omega_R$) protects the qubit against low-frequency noise during transport.
• Figure 2: Qubit as a sensor of the noise landscape. Results of Ramsey-style dephasing measurements for a stationary qubit as a function of position along the conveyor. Red and blue data correspond to the standard high-field (260mT) and demagnetized low-field (-30mT) setups, respectively. (a) Fitted dephasing time, $T_2^*(x_n)$ (solid lines are added for guidance). (b) Relative qubit frequency with respect to the corresponding minima $(\omega_q-\omega_\text{min})/2\pi$, along the conveyor obtained through EDSR (high-field) and Ramsey spectroscopy (low-field). For the underlying data, extracted exponents and fits to the decoherence curves, see Appendix \ref{['app:two_points_data']}
• Figure 3: Spatial noise correlations. Two-point Ramsey measurement of the dephasing time $T_{2}^{*,0n}(x_n)$ as a function of the variable position $x_n$, with the other point fixed at $x_0$. The fitted dephasing time is plotted as square data points with error bars, along with an interpolated trend (solid line). This is compared to an uncorrelated noise model (dashed line) derived from stationary data. The shaded region is the difference between the two with red color indicating correlations and blue negative correlations. The top/bottom subpanels show the extracted noise correlation coefficient $r_{0n}$. The inset diagram in (a) illustrates the pulse sequence, where an evolution time $\tau/2$ is spent at each location. Panel (a) corresponds to the high-field (260mT) case, and panel (b) to the low-field (-30mT) case. For the underlying data and fits to the decoherence curves, see Appendix \ref{['app:two_points_data']}.
• Figure 4: Coherence during periodic shuttling. The panels show several spin coherence times measured during continuous back-and-forth shuttling, as a function of shuttling distance $d$. The inset in (b) schematically illustrates the shuttling protocol. Measured coherence times are extracted from experiments using a Ramsey-style pulse sequence (circles), a Hahn-echo sequence (squares), and a three-pulse CPMG sequence (triangles), with interpolated lines for guidance. The Ramsey results are compared to a theoretical model (dashed lines) derived from stationary data and a finite correlation length. Panel (a) shows the high-field case, and panel (b) the low-field case. For underlying data and fits to decoherence curves, see Appendix \ref{['app:shuttling_data']}.
• Figure 5: Dressed-state shuttling experiments. (a) Schematic of the experiment in which we periodically shuttle the electron in the presence of a transverse gradient on resonance with the average spin-splitting. In the rotating frame this results in a periodic drive through an avoided crossing, given by the drive amplitude $A_{mw}$. (b) Return probability showing resonant Landau-Zener-Stückelberg-Majorana (LZSM) sidebands as a function of microwave drive and shuttling frequency (high-field). (c) Measured Rabi decay time $T_R^{sh}$ as a function of the Rabi frequency $\Omega_R/2\pi$ for different shuttling distances in the high-field (red) and low-field regime (blue). In the low-field regime, different $\Omega_R$ are obtained by adjusting the gate voltages. (d) Ratio $T_R^{sh} / \Omega_R$, extracted from the linear fits in panel (c), as a function of shuttling distance $d$ (points). The dashed line represents a theoretical upper bound derived from $T_2^{CPMG,sh}$ data obtained in the shuttling experiment (see Appendix \ref{['app:coherence_in_driven']} for details). The inset relates shuttling distances $d$ to the spin splitting landscape.