Disorder-independent hole spin manipulation by hopping

Abstract

Spin manipulation by hopping has recently emerged as a promising strategy to control hole spins in quantum dots using exclusively baseband control, thereby mitigating power dissipation and high-frequency management constraints in large-scale architectures. Unlike conventional approaches such as electron dipole spin resonance (EDSR), this mechanism exploits dot-to-dot variations of the spin precession axes to enable spin rotations. However, it is intrinsically disorder-dependent: in the absence of sufficient variability, the precession axes remain aligned and spin manipulation becomes ineffective. This fundamental reliance on disorder raises concerns regarding its compatibility with the long-term evolution of spin-qubit platforms toward improved material quality, cleaner interfaces, and enhanced device reproducibility. Here, we numerically assess the viability of spin manipulation by hopping as a function of disorder strength and demonstrate that its implementation is indeed increasingly constrained as disorder is reduced. To overcome this limitation, we propose an alternative strategy based on hopping between intentionally squeezed quantum dots. This approach retains the advantages of baseband control while being independent of disorder and robust against moderate variability, thereby offering improved prospects for scalable hole-spin quantum computing architectures.

Figures (19)

• Figure 1: a) The array of Ge hole spin qubits. SiGe is shown in light purple, Ge in dark purple, and the aluminium gates in gray. The dashed black line delimits the minimal unit cell of the array, and the solid black line the supercell considered for single QD calculations. The inset illustrates a top view of a double QD, where the two dots (orange) are deformed by the charged defects (green) with respect to the pristine QD (yellow). As a consequence, their magnetic axes $\boldsymbol{v}_1$, $\boldsymbol{v}_2$ (and $\boldsymbol{v}_3$) are scattered. b) Definition of the magnetic angles $(\theta_v,\varphi_v)$ describing the tilt of the magnetic axes $\{\boldsymbol{v}_1,\boldsymbol{v}_2,\boldsymbol{v}_3\}$ with respect to the device axes, and of the Larmor angles $(\theta_L,\varphi_L)$ characterizing the orientation of the Larmor vector. c) The Larmor angle $\theta_L$ as a function of the orientation of the magnetic field $\boldsymbol{B}=|\boldsymbol{B}|(\sin\theta\cos\varphi,\sin\theta\sin\varphi,\cos\theta)$ for a pristine QD ($V_C=-57.4$ mV and all other gates grounded). d) The Larmor angle $\theta_L$ as a function of $\theta$ for $\varphi=0\degree$ (cut along the vertical dashed line in c)).
• Figure 2: Scattering of Larmor angles in the presence of disorder in nominally circular QDs with size $\ell_c^0=20$ nm. a) Histogram of the magnetic angles $(\theta_v,\varphi_v)$, principal $g$ factors $(g_1,g_2)$, and Larmor angles $(\theta_L,\varphi_L)$ in disordered QDs with charge trap density $n_i=10^{11}$ cm$^{-2}$. The orange lines are the values for the pristine device. b) Inter-quartile range ($\mathcal{R}$) of the Larmor angles as a function of the magnetic field orientation. c) Dependence of the inter-quartile range of the Larmor angles on $n_i$. The dashed lines are guides to the eye for the expected $\propto\sqrt{n_i}$ dependence Martinez2022. In panels a) and c), $\theta_L$ and $\varphi_L$ and calculated for a magnetic field $\boldsymbol{B}\parallel\boldsymbol{x}$.
• Figure 3: Statistics of the angle between the Larmor vectors of pairs of nominally circular QDs with size $\ell_c^0=20$ nm. a) Histogram of the angle $\alpha$ between the Larmor vectors of QD pairs ($\boldsymbol{B}\parallel\boldsymbol{x}$), for charge trap densities $n_i=10^{11}$ cm$^{-2}$ (top panel) and $n_i=10^{10}$ cm$^{-2}$ (bottom panel). b) Dependence of the median $\overline{\alpha}$ (top panel) and inter-quartile range $\mathcal{R}(\alpha)$ (bottom panel) on the magnetic field angle $\theta$ for $\varphi=0\degree$. The trends are rather independent on $\varphi$. c) Dependence of $\overline{\alpha}$ and $\mathcal{R}(\alpha)$ on $n_i$ ($\boldsymbol{B}\parallel\boldsymbol{x}$).
• Figure 4: Statistics on the Rabi frequencies and number of shuttling pulses. a) Histogram of the Rabi frequency $f_R$ and number of shuttling pulses $n_\pi$ required to perform a $\pi$ rotation of the spin for disordered QDs with charge trap density $n_i=10^{11}$ cm$^{-2}$. b) Median (top panel) and inter-quartile range (bottom panel) of $f_R$ and $n_\pi$ as a function of $n_i$. In all panels, $\ell_c^0=20$ nm and $\boldsymbol{B}\parallel\boldsymbol{x}$.
• Figure 5: Percentage of functional quantum dot pairs (yield) as a function of the charge trap density $n_i$. The functionality condition is $f_R>f_R^{\rm min}$ for the top panel, and $n_\pi<n_\pi^{\rm max}$ for the bottom panel. For all $n_i$, $\ell_c^0=20$ nm and $\boldsymbol{B}\parallel\boldsymbol{x}$.