Protocol for nearly deterministic parity projection on two photonic qubits

Photonic parity projection plays an important role in photonic quantum information processing. Nondestructive parity projections normally require high-fidelity controlled-<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>Z</a:mi></a:math> 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. We also demonstrate that our protocol can tolerate moderate Gaussian phase errors in the controlled-phase gates as well as Pauli errors on the matter qubits. The fact that our protocol does not require perfect controlled-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>Z</b:mi></b:math> gates makes it more amenable to experimental implementation. Although we focus on photonic qubits, our protocol can be applied to any physical system or circuit with imperfect controlled-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>Z</c:mi></c:math> gates. Our protocol also provides a new optimization space for parity projection operations on various physical platforms, which is potentially beneficial for achieving high-fidelity parity projection operations. Published by the American Physical Society 2024