Linear optical fan-out gates using fewer ancillary single photons with enhanced success probability

Photonic quantum gates are fundamental building blocks for a wide range of optical quantum information processing tasks. We propose an efficient linear-optical scheme for implementing a post-selected three-qubit fan-out gate (also known as a controlled-NOT-NOT gate) using only two ancillary single photons and linear optical elements. The scheme can be generalized to an $n$-qubit fan-out gate, requiring $(n-1)$ ancillary single photons and $(3n-3)$ polarizing beam splitters (PBSs), with a success probability of ${\left(\frac{1}{4}\right)}^{n-1}$. Compared to the standard gate decomposition approach, which requires $(2n-2)$ ancillary single photons, $(5n-5)$ PBSs, and yields a success probability of ${\left(\frac{1}{8}\right)}^{n-1}$. Our scheme significantly reduces the resource overhead and improves the success probability. We further evaluate the gate performance and demonstrate improved robustness compared to gate decomposition-based methods.