Nonadiabatic controlled-NOT gate for the Kane solid-state quantum computer

Abstract

An effective Hamiltonian that describes the interaction of the qubits in the subspace of the electron ground state was developed using the method of iterated resolvent. This effective Hamiltonian was then used to derive a controlled-NOT gate that relies only on the evolution of the qubits that it generates, in combination with the single-qubit operations. This fact was then used to argue that the family of gates consisting of the free evolution of neighboring qubits for predetermined times, is a suitable alternative to the adiabatically constructed c-NOT gate for use in the implementation of quantum algorithms.