Error rate of the Kane quantum computer controlled-NOT gate in the presence of dephasing

Abstract
We study the error rate of controlled-NOT (CNOT) operations in the Kane solid-state quantum computer architecture [B. Kane, Nature 393, 133 (1998)]. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off-diagonal elements of the system’s density matrix. Using available spin-echo decay data, the CNOT error rate is estimated at 103.