  Photonic parity projection plays a significant role in photonic quantum
information processing. Non-destructive parity projections normally require
high-fidelity Controlled-Z gates between photonic and matter qubits, which can
be experimentally demanding. In this paper, we propose a nearly deterministic
parity projection protocol on two photonic qubits which only requires stable
matter-photon Controlled-Phase gates. The fact that our protocol does not
require perfect Controlled-Z gates makes it more amenable to experimental
implementation.
