Quantum computing with spin qubits interacting through delocalized excitons: Overcoming hole mixing

As a candidate scheme for controllably coupled qubits, we consider two quantum dots, each doped with a single electron. The spin of the electron defines our qubit basis and trion states can be created by using polarized light; we show that the form of the excited trion depends on the state of the qubit. By using the Luttinger-Kohn Hamiltonian we calculate the form of these trion states in the presence of light-heavy hole mixing, and show that they can interact through both the Förster transfer and static dipole-dipole interactions. Finally, we demonstrate that by using chirped laser pulses, it is possible to perform a two-qubit gate in this system by adiabatically following the eigenstates as a function of laser detuning. These gates are robust in that they operate with any realistic degree of hole mixing, and for either type of trion-trion coupling.

Figure 1

(Color online) Hole states in the presence of hole subband mixing and its effect on Pauli blocking. The arrows denote the allowed optical interband transitions for an incoming ${\sigma }^{+}$ polarized laser pulse. The left part of the figure represents the situation where no hole mixing is present and the right-hand side shows the effects of mixing.

Figure 2

(Color online) Eigenstate energy spectrum. The parameters are set as follows: $\delta ∕\Omega =1$, $M_{hh,hh}∕\Omega =M_{lh,hh}∕\Omega =0.5$, $V_{XX}∕\Omega =2$, $ϵ=0.1$.

Figure 3

Variation of $\theta$ [Eq. (47)] as a function of time. The parameters are set as follows: $\delta =1\mathrm{meV}$, $M_{hh,hh}=M_{lh,hh}=0.5\mathrm{meV}$, $V_{XX}=2\mathrm{meV}$, $ϵ=0.1$, ${\tau }_{\Omega }=3.55\mathrm{ps}$, ${\tau }_{\Delta }=2.55\mathrm{ps}$, ${\Delta }_0=4.5\mathrm{meV}$, and ${\Omega }_0=8\mathrm{meV}$.

Figure 4

(Color online) Variation of the initial state population for each computational basis state during a gate operation. The parameters are the same as in Fig. 3.

Figure 5

Variation of $\theta$ [Eq. (47)] as a function of time. The parameters are set as follows: $\delta =1\mathrm{meV}$, $M_{hh,hh}=M_{lh,hh}=0.5\mathrm{meV}$, $V_{XX}=0$, ${\Omega }_0=8\mathrm{meV}$, ${\tau }_{\Omega }=4.2\mathrm{ps}$, ${\tau }_{\Delta }=3\mathrm{ps}$, ${\Delta }_0=3\mathrm{meV}$, and $ϵ=0.1$.

Figure 6

(Color online) Variation of the initial state population for each computational basis state during a gate operation. The parameters are the same as in Fig. 5.