Implementation of Shor’s algorithm with a single photon in 32 dimensions

Photonics has been a promising platform for implementing quantum technologies owing to its scalability and robustness. In this paper, we demonstrate the encoding of information in 32 time bins or dimensions of a single photon. A practical scheme for manipulating the single photon in high dimensions is experimentally realized to implement a compiled version of Shor's algorithm on a single photon. Our work demonstrates the powerful information-processing capacity of a high-dimensional quantum system for complex quantum information tasks.