Role of hyperfine interaction for cavity-mediated coupling between spin qubits

Abstract

We consider two qubits interacting by means of an optical cavity, where each qubit is represented by a single-electron spin confined to a quantum dot. It is known that electron spins in III-V semiconductor quantum dots are affected by the decoherence due to the hyperfine interaction with nuclear spins. Here we show that the interaction between two qubits is influenced by the Overhauser field as well. Starting from an unpolarized nuclear ensemble, we investigate the dependance of the fidelities for two-qubit gates on the Overhauser field. We include the hyperfine interaction pertubatively to second order in our analytical results and to arbitrary precision numerically.