Implementation of General Qubit‐quNit Quantum Computation

Abstract A high‐dimensional system, so‐called quNit (‐level quantum system with ), provides several unique advantages, and high‐precision manipulation of arbitrary single‐quNit is demonstrated. In this study, a program to construct arbitrary qubit‐quNit quantum computation up to a global phase, and an efficient construction that requires single‐particle and generalized controlled (GCX) gates in the worst case are proposed. Moreover, by encoding the computing basis in polarization and spatial degrees of freedom of a single‐photon state, the optical architectures to implement the elementary‐gate library GCX, single‐partite rotation in a high‐dimension system are designed using linear optics. The necessary single‐photon polarization state and flexibility of linear optical elements make the quantum circuit feasible with current experimental technologies.