Photon-Loss Effects on the Efficiency of Quantum Linear-Optical Gates and Cluster States

Linear optical quantum computing in the dual-rail representation offers the practical advantage of room-temperature operation, with quantum gates implemented through beam splitters and phase shifters. Despite its appeal, this approach is fundamentally constrained by the non-deterministic nature of entangling gates, which limits scalability within the circuit-based paradigm. Measurement-based quantum computation (MBQC) addresses this issue by employing pre generated cluster states and single-qubit projective measurements, but both frameworks remain highly susceptible to photon loss, the dominant error in photonic systems. In this work, we investigate the effects of photon loss on single-qubit gates, heralded two-qubit entangling gates, the two-qubit Grover algorithm, and the preparation of a three-qubit cluster state. By employing simplified photon-loss models, we quantify both the success probability and fidelity degradation of the resulting states. These results provide practical insight into the limitations of current photonic architectures and highlight pathways toward efficient error mitigation in near-term quantum technologies.