Charge qubits in semiconductor quantum computer architecture: Tunnel coupling and decoherence

We consider charge qubits based on shallow donor electron states in silicon and coupled quantum dots in GaAs. Specifically, we study the feasibility of $P_2^{+}$ charge qubits in Si, focusing on single qubit properties in terms of tunnel coupling between the two phosphorus donors and qubit decoherence caused by electron-phonon interaction. By taking into consideration the multivalley structure of the Si conduction band, we show that intervalley quantum interference has important consequences for single-qubit operations of $P_2^{+}$ charge qubits. In particular, the valley interference leads to a tunnel-coupling strength distribution centered around zero. On the other hand, we find that the Si band structure does not dramatically affect the electron-phonon coupling and consequently, qubit coherence. We also critically compare charge qubit properties for $\mathrm{Si}:P_2^{+}$ and GaAs double quantum dot quantum computer architectures.

Figure 1

(Color online) Symmetric-antisymmetric gap for the $P_2^{+}$ molecular ion in Si for the donor pair along the indicated lattice directions. The arrow in the upper frame indicates the target configuration analyzed in Fig. 2.

Figure 2

(Color online) Probability distributions of the symmetric-antisymmetric gap for the $P_2^{+}$ molecular ion in Si. Donor pairs are approximately aligned along [100], but with an uncertainty radius $R_u$ with respect to this target axial alignment (see text). The arrow in each panel indicates the gap value for the target configuration, for which the uncertainty radius is $R_u=0$. Notice that all four distributions are peaked at ${\Delta }_{S-AS}=0$, and not at the target gap value.

Figure 3

(Color online) Energy gap between the ground and first excited states of a single electron double dot as a function of interdot distance. The crosses are for two identical dots with a fixed Gaussian confinement (see Ref. 41) (with a ground orbital radius of 12.6 nm); the squares are for situations where one dot is 5% larger; the triangles are for situations where that same dot is 5% smaller. At larger interdot distances the different-dot configurations have larger energy splittings because the dot size difference introduces an energy level detuning that is larger than the tunnel coupling. The inset plots the same data in the range of 30–34 nm interdot distance in the linear scale, where we find that the 5% dot size variation leads to a 10%–20% difference in the tunnel coupling.