Controllability of multiple qubit systems

This paper explores the problem of manipulating multiple-qubit systems when only single-qubit operations or two-qubit-interactive operations are permitted. It is demonstrated that if there exist 2 directional control Hamiltonian for each individual qubit, and one interactive Hamiltonian for each pair of qubits, then multiple qubit systems are open-loop controllable. An important observation of physical interest is emphasized: when only single-qubit operations or two-qubit-interactive operations are permitted, only n(n+3)/2 control Hamilton may guarantee open-loop controllability of n qubit systems, and n(n+3) is, in the restricted sense, also the lower limit on the number of operators needed for controllability. At last, we demonstrate that an n-quantum-dot system is open-loop controllable even when only single-qubit operations or two-qubit-interactive operations are permitted.