Cost Analysis of Manipulating Multiple Qubit Systems

For a multiple qubit system, the dimension of the system is exponentially large in the number of qubits, one may ask whether the cost of manipulating multiple qubit systems is exponentially large in the number of qubits or not? It has been found that only n(n + 3)/2 control Hamilton will guarantee open-loop controllability of n-qubit systems when only single qubit operators and two-qubit-interactive operators are permitted. Further more, the minimum cost of deterministically generating multiple-qubit GHZ entangled state will be at most linearly large in the number of qubits. To some extent, one may predict that the "cost" of manipulating multiple-qubit systems is tolerable.