Enhancing the W State Fusion Process With a Toffoli Gate and a CNOT Gate via One-Way Quantum Computation and Linear Optics

Creation of large-scale W state quantum networks is a key step for realization of various quantum information tasks.Regarding the photonics technology, a simple optical setup was proposed for the fusion of two W states.Recently it was shown that via a single Fredkin gate, this basic so-called fusion setup can be enhanced.However the main problem was that the probability of success of realization of Fredkin gate with linear optics is too low.In this work, we show that the same enhancement can be made possible via one Tooli and one CNOT gate, instead of a Fredkin gate.Not only the probability of success of the combination of these two gates is much higher, than that of a single Fredkin gate via linear optics, but also there is another method for implementing our setup with current photonics technology, almost with a unity success probability: A hybrid circuit consisting of a Tooli gate which can be implemented via one-way quantum computation on a weighted graph state of 8 qubits with a unity success probability and a linear optical CNOT gate which has a success probability close to unity.Therefore the preparation of polarization based encoded multi particle entangled W states of arbitrary sizes becomes considerably more ecient.