Noise Suppression Using Symmetric Exchange Gates in Spin Qubits

We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.

Figure 1

(a) Schematic comparison of detuning (tilt) and symmetric exchange pulse sequences, showing double-dot potentials and dot occupancies. Tilt, wave function overlap controlled by detuning the confining potential. Symmetric, wave function overlap controlled by lowering the potential barrier between dots. (b) Electron micrograph of the device consisting of a double dot and charge sensor. Note the gate that runs through the center of the dots. A 10 nm ${\mathrm{HfO}}_2$ layer is deposited below the gates to allow positive and negative gating. High-bandwidth lines are connected to left and right plungers gates $V_L$, $V_R$ (blue), and the middle barrier gate $V_M$ (red). (c) Energy diagrams of the two-electron spin singlet, $S$, and spin-zero triplet, $T_0$, as a function of detuning $ϵ$. (Left) Tilt mode, exchange $J$ is controlled by detuning $ϵ$, set by $V_L$ and $V_R$. (Right) Symmetric mode, $J$ is controlled interdot coupling $\gamma$ set by $V_M$ (red curve). (d) Pulse sequences for tilt and symmetric modes, with amplitudes ${ϵ}_x$ and ${\gamma }_x$ during the exchange pulse, respectively.

Figure 2

(a) Probability of detecting a singlet $P_s$ as a function of ${ϵ}_x$ and exchange time $\tau$ for tilt-induced oscillations (${\gamma }_x=0\mathrm{mV}$). (b) $P_s$ as a function of ${\gamma }_x$ and exchange time $\tau$ obtained for barrier-induced oscillations near the symmetry point (${ϵ}_x=13.5\mathrm{mV}$). (c) Same as (a) with barrier pulse activated, ${\gamma }_x=190\mathrm{mV}$, revealing the sweet spot of the symmetric operation. The dark vertical features near 39 and $-44\mathrm{mV}$ are due to leakage from the singlet state to the spin-polarized triplet state. Insets show theoretical simulations for each experimental situation.

Figure 3

(a) Tilt-induced exchange oscillations (i.e., ${\gamma }_x=0\mathrm{mV}$) for ${ϵ}_x=79.5$ and 82 mV, generating oscillation frequencies indicated by $J$. (b) Same as (a) but for the symmetric mode of operation (${ϵ}_x=13.5\mathrm{mV}$), with ${\gamma }_x=100$, 120, and 140 mV. Open circles are experimental data. Solid lines correspond to the theoretical model in Eq. (2), with $J$ and a horizontal offset being the only adjustable parameters. Insets show the quality factor $Q$, defined as the number of oscillations before the amplitude damps by a factor of $e$, as a function of $J$ for both tilt and symmetric operation modes. Solid circles correspond to data in the main panel, and solid lines are theoretical predictions.

Figure 4

(a) Saturation probability of the symmetric mode of operation $P_{\mathrm{sat}}$ as a function of $J$ (symbols). Comparison with theory (solid line) determines $T_{RM}$ and $h_0$. (b) Plot of ${ϵ}_x$ for the tilt and ${\gamma }_x$ for the symmetric mode of operation, as functions of the exchange coupling extracted experimentally. (c) Decoherence time $T_R$, i.e., time before the amplitude of oscillations is reduced by a factor of $e$, as a function of $J$ for both tilt and symmetric modes. (d) Quality of the exchange rotations, defined as $Q=J{T}_R$, for different $J$. In (c) and (d) the open circles are obtained experimentally and solid lines correspond to a model that includes dephasing due to electrical and nuclear noise. Black dashed lines are the same model if we only consider nuclear noise contributions ($T_R^{(\mathrm{nuc})}$, $Q^{(\mathrm{nuc})}$). Blue and red dashed lines correspond to the electrical noise contributions ($T_R^{(\mathrm{el})}$, $Q^{(\mathrm{el})}$) for the tilt and symmetric modes of operation, respectively. The solid circle indicates the maximum $Q$ value observed in Fig. 2.