Quantum Optical Approach to the $K$ Nearest Neighbour Algorithm

We construct a hybrid quantum-classical approach for the $K$-Nearest Neighbour algorithm, where the information is embedded in a phase-distributed multimode coherent state with the assistance of a single photon. The task of finding the closeness between the data points is delivered by the quantum optical computer, while the sorting and class assignment are performed by a classical computer. We provide the quantum optical architecture corresponding to our algorithm. The subordinate optical network is validated by numerical simulation. We also optimize the computational resources of the algorithm in the context of space, energy requirements and gate complexity. Applications are presented for diverse and well-known public benchmarks and synthesized data sets.