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We propose a quantum circuit composed of $cNOT$ gates and four single-qubitgates to generate a $W$ state of three qubits. This circuit was then enhancedby integrating two-qubit gates to create a $W$ state of four and five qubits.After a couple of enhancements, we show that an arbitrary $W$ state can begenerated depending only on the degree of enhancement. The generalized formulafor the number of two-qubit gates required is given, showing that an $n$-qubit$W$-state generation can be achieved with quadratically increasing number oftwo-qubit gates. Also, the practical feasibility is discussed regarding photonsources and various applications of $cNOT$ gates.

Deterministic construction of arbitrary $W$ states with quadratically increasing number of two-qubit gates