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.