Feasibility of the controlled-NOT gate from certain model Hamiltonians

The controlled-NOT (CNOT) gate is widely used in quantum circuits and in current and proposed quantum computing technologies. We investigate the feasibility and minimal implementation of CNOT from specific model Hamiltonian operators that have appeared in the literature. We follow an algebraic approach that provides an analytic solution. Our results are relevant to effective two-qubit Hamiltonians currently being considered for spin-based, superconductivity-based and other implementations of quantum computing