Deterministic construction of arbitrary <i>W</i> states with quadratically increasing number of two-qubit gates

We propose a quantum circuit composed of cNOT gates and four single-qubit gates to generate a W state of three qubits. This circuit was then enhanced by 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 be generated depending only on the degree of enhancement. The generalized formula for the number of two-qubit gates required is given, showing that an n-qubit W-state generation can be achieved with quadratically increasing number of two-qubit gates. The practical feasibility is discussed regarding photon sources and various applications of cNOT gates. In addition, we discuss possible future directions for quantum-state networks, concerning quantum correlations of W states. (c) 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/).