Quadrupolar Exchange-Only Spin Qubit

We propose a quadrupolar exchange-only spin qubit that is highly robust against charge noise and nuclear spin dephasing, the dominant decoherence mechanisms in quantum dots. The qubit consists of four electrons trapped in three quantum dots, and operates in a decoherence-free subspace to mitigate dephasing due to nuclear spins. To reduce sensitivity to charge noise, the qubit can be completely operated at an extended charge noise sweet spot that is first-order insensitive to electrical fluctuations. Because of on-site exchange mediated by the Coulomb interaction, the qubit energy splitting is electrically controllable and can amount to several GHz even in the “off” configuration, making it compatible with conventional microwave cavities.

Figure 1

(a) Illustration of a four-electron spin qubit residing in an electrostatically defined triple quantum dot (TQD). The four spins are coupled via interdot and on-site exchange interaction. The center dot is occupied by two electrons, giving rise to a large and electrostatically tunable energy splitting. (b) TQD charge stability diagram as a function of $ϵ$ and ${ϵ}_M$. The optimal operating point is marked by the star.

Figure 2

Qubit basis states and TQD confining potential $V(x)$. The left and right dots each contain one electron in the ground state (black level). The middle dot contains two electrons, one of which can occupy an excited valley state (gray level), lying $E_{V,C}$ above the ground state. The electrons are allowed to hop with valley conserving (green $t_{l,r}$), and valley nonconserving (blue $t_{l,r}^{\prime }$) tunneling. (a) Possible spin configuration of the qubit state $|0⟩$. Inset: Spin configuration in the center dot. Both electrons reside in the valley ground state. (b) Possible spin configuration of the qubit state $|1⟩$. Inset: Spin configuration in the center dot. One electron resides in the valley ground state while the second electron occupies an excited valley state.

Figure 3

Protocol for initializing the QUEX qubit. First the (2,0,2) charge configuration (a) is prepared by loading the left and right QD with two electrons in the spin-up and spin-down state of the lowest valley. (b) Adiabatic tuning from the (2,0,2) to the (1,2,1) charge state directly maps $|\mathrm{init}⟩\to |1⟩$. Readout is performed by reversing the initialization sequence, as described in the main text.

Figure 4

Qubit energy splitting $\omega$ as a function of (a) the dipolar detuning $ϵ$ and (b) quadrupolar detuning ${ϵ}_M$. The stars in (a) and (b) mark the sweet spots where $\partial {\omega }_q/\partial ϵ=0$ and $\partial {\omega }_q/\partial {ϵ}_M=0$. For comparison, the energy gap ${\omega }_{\mathrm{EO}}$ of the conventional exchange-only (EO) qubit (gray dashed lines) is shown with identical parameter settings. The curvature of ${\omega }_{\mathrm{EO}}$ is larger in magnitude causing a higher susceptibility to charge noise. (c) Qubit dephasing time $T_{\phi }$ due to charge fluctuations as a function of $ϵ$ and ${ϵ}_M$ for $t_l^{\prime }=t_r^{\prime }$ using realistic parameters [55]. The calculations show that $T_{\phi }>100\mu \mathrm{s}$ if the qubit is operated at the charge noise sweet spot. (d) Qubit dephasing time for the conventional exchange-only qubit with identical parameter settings. Expressions for the calculation of $T_{\phi }$ can be found in Refs. [21, 22]. (e) Schematic of the microwave resonator mediated two-qubit coupling. A cavity with resonance frequency ${\omega }_{\mathrm{res}}$ is coupled to the center dot with an effective charge-cavity coupling rate $g_{c,i}$. Each qubit is simultaneously driven at a frequency ${\omega }_{D,i}$.