Scheme for Universal High-Dimensional Quantum Computation with Linear Optics

Photons are natural carriers of high-dimensional quantum information, and, in principle, can benefit from higher information capacity and noise-resilience. However, schemes to generate the resources required for computing have so far been lacking linear optics. Here, we show how GHZ states arbitrary dimensions numbers photons using optical circuits described by Fourier transform matrices. Combining our results with recent qudit Bell measurements, that universal be performed dimensions.