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 Letter, 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.