Tunable Spin-Qubit Coupling Mediated by a Multielectron Quantum Dot

We present an approach for entangling electron spin qubits localized on spatially separated impurity atoms or quantum dots via a multielectron, two-level quantum dot. The effective exchange interaction mediated by the dot can be understood as the simplest manifestation of Ruderman-Kittel-Kasuya-Yosida exchange, and can be manipulated through gate voltage control of level splittings and tunneling amplitudes within the system. This provides both a high degree of tunability and a means for realizing high-fidelity two-qubit gates between spatially separated spins, yielding an experimentally accessible method of coupling donor electron spins in silicon via a hybrid impurity-dot system.

Figure 1

(a) Charge stability diagram for the combined impurity-dot three-site model ($U\equiv U_1$, ${\epsilon }_m\equiv {\epsilon }_1$), with the operating point indicated. (b) Schematic diagram showing the orbitals of a pair of single-level impurity atoms coupled via a two-level quantum dot. The electron occupation illustrates the initial configuration (1, 2, 1). Arrows depict the tunneling amplitudes defined in Eq. (2). Reversing the direction of an arrow corresponds to taking the complex conjugate of the associated tunneling amplitude. (c) Energy level diagram illustrating the two-spin states of the mediator dot used in our calculation.

Figure 2

Schematic illustration of virtual tunneling processes which give rise to the effective exchange interaction in Eq. (6). The red (blue) arrows correspond to the process in which the electron in orbital $L$ ($R$) tunnels to the center dot in the first step. Each step is labeled with the tunnel coupling for the associated hopping term in $H_t$ [Eq. (2)], and the zeroth-order energies of the charge configurations [Eqs. (3)–(5)] are indicated.

Figure 3

Minimum fidelity [Eq. (7)] of the square-root-of-swap exchange gate $U_{\text{sw}}^{1/2}\equiv \widehat{U}(\pi /2J)$ as a function of the quantum-dot level splitting ${\mathrm{\Delta }}_M$ and impurity-dot detunings ${\mathrm{\Delta }}_L={\mathrm{\Delta }}_R\equiv {\mathrm{\Delta }}_I$ for ${\sigma }_L={\sigma }_R={\sigma }_M=2\mu \mathrm{eV}$, $T_2^{*}=1\mathrm{ms}$ [61, 62], and $|t_{Li}|=|t_{Ri}|=t=2\mu \mathrm{eV}$ [63].