Quantum operations on charge qubits with the electrostatic control in semiconductor cavities

We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.