Protocols for nearly deterministic parity projection on two photonic qubits

Parity projection plays an important role in quantum computing and quantum information processing, especially for photonic systems. The previous attempts to apply parity projection measurements on photonic qubits rely on using probabilistic fusion gates. We present a robust protocol for a nearly deterministic parity projection on two photonic qubits with the help of a matter qubit. The protocol can increase the success probability of linear optical quantum computing schemes. It can also improve the efficiency of generating large graph states by fusing.