Fully Tunable Hyperfine Interactions of Hole Spin Qubits in Si and Ge Quantum Dots

Hole spin qubits are frontrunner platforms for scalable quantum computers, but state-of-the-art devices suffer from noise originating from the hyperfine interactions with nuclear defects. We show that these interactions have a highly tunable anisotropy that is controlled by device design and external electric fields. This tunability enables sweet spots where the hyperfine noise is suppressed by an order of magnitude and is comparable to isotopically purified materials. We identify surprisingly simple designs where the qubits are highly coherent and are largely unaffected by both charge and hyperfine noise. We find that the large spin-orbit interaction typical of elongated quantum dots not only speeds up qubit operations, but also dramatically renormalizes the hyperfine noise, altering qualitatively the dynamics of driven qubits and enhancing the fidelity of qubit gates. Our findings serve as guidelines to design high performance qubits for scaling up quantum computers.

Figure 1

Gaussian decay time $T_0$ in idle qubits in rectangular wires. We examine Si (solid lines) and Ge (dashed lines) dots when $E_y=0$ and show $T_0$ for different directions of $\mathbf{B}$ as a function of $L_x/L_y$. In (a) and (b), we study wires grown along the CA and DRA, respectively. Confinement (crystallographic) axes are shown with black (blue) arrows.

Figure 2

Tunability of the hyperfine interactions. In (a) and (b), we show $T_0$ against $E_y$ in Si wires grown along the DRA with square and equilateral triangular cross sections, respectively. $E_y$ is measured in units of ${\epsilon }_c/eL\approx 3.22\times (L/10\mathrm{nm}{)}^{-3}\mathrm{V}/\mu \mathrm{m}$. Solid (dashed) lines represent results that include (neglect) DRSOI, see Eq. (5). In (b) we include the decay times $T_0^{\mathrm{SA}}$ of qubits in SA wires (thin dashed lines); $l_{\mathrm{SO}}/L$ is shown in dashed gray lines. In (c), we show the $g$ factors in triangular and square wire qubits. Black, blue, red lines correspond to $\mathbf{B}$ aligned to $x$, $y$, $z$ direction, respectively, and we use $l_z=L$. In (d), we include high energy states in triangular wires and compare cross sections having different aspect ratios $r$ and the same area ${\mathcal{A}}_{\rho }=\sqrt{3}{L}^2/4$. Here, $L=30\mathrm{nm}$.

Figure 3

Spin decay during qubit operations. In (a) we show the relevant decay times when $\mathbf{B}\parallel y$ (blue) and $\mathbf{B}\parallel z$ (red) of a qubit in a Si square wire grown along the DRA. Here, $l_z=L$, ${\omega }_B/2\pi =3\mathrm{GHz}$, $N={10}^4$, and $d_0=0.02l_z$, resulting in ${\omega }_R^{\max }/2\pi \approx 75\mathrm{MHz}$. In (b) we consider $E_y=6{\epsilon }_c/eL$ and study the spin decay of the Rabi oscillations and its deviation from purely Gaussian and power-law scaling.