Electrically Protected Resonant Exchange Qubits in Triple Quantum Dots

We present a modulated microwave approach for quantum computing with qubits comprising three spins in a triple quantum dot. This approach includes single- and two-qubit gates that are protected against low-frequency electrical noise, due to an operating point with a narrowband response to high frequency electric fields. Furthermore, existing double quantum dot advances, including robust preparation and measurement via spin-to-charge conversion, are immediately applicable to the new qubit. Finally, the electric dipole terms implicit in the high frequency coupling enable strong coupling with superconducting microwave resonators, leading to more robust two-qubit gates.

Figure 1

(a) Schematic of a triple quantum dot with one electron per dot—the (1, 1, 1) charge configuration. (b) Charge stability diagram for a lateral triple dot with $U_c=0.3$ $U$, $V_{\mathrm{tot}}=2.6U$, $t_l=t_r=0$ as a function of $ϵ/U$, $V_m/U$ where $U\sim 1–10\mathrm{meV}$. As $V_m$ increases the width of the (201)-(111)-(102) region decreases, and the dashed box indicates the regime of interest for (c); other charging numbers are not shown. (c) Energy levels at high external magnetic field $g^{*}{\mu }_B{B}_{\mathrm{ext}}\gg t$) for the $m_s=1/2$ subspace as a function of $ϵ$ for fixed $\Delta =3t$ in units of $t=t_l=t_r$.

Figure 2

(a) Virtual process that leads to an electric dipole element between the two logical states, where tunneling couples to the symmetric (antisymmetric) combination of excited charge states, which are in turn coupled by electric field. (b)–(d) Dipole-dipole coupling, near-field multipole coupling, and coupling to a superconducting transmission line resonator. (e) Contour plot of phonon-induced relaxation $\Gamma$ between logical states at the operation point ${ϵ}_0=0$, as a function of the qubit frequency $\omega$ and the charge admixture parameter $\xi =t/\Delta$. Quantities used to calculate $\Gamma$ include the Gaussian width parameter $\sigma =20\mathrm{nm}$, $a=260\mathrm{nm}$, and phonon parameters relevant for GaAs quantum dots [44], including ${\rho }_0=5.3\times {10}^3\mathrm{kg}/{\mathrm{m}}^3$, $c_l=5.3\times {10}^3\mathrm{m}/\mathrm{s}$, $c_t=2.5\times {10}^3\mathrm{m}/\mathrm{s}$, ${\beta }_l=7.0\mathrm{eV}$, and $\Xi =1.4\times {10}^9\mathrm{eV}/\mathrm{m}$. The inset shows how electric dipole coupling to the cavity also leads to phonon-based decay.