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

Automated summary

The study demonstrates how to generate GHZ states in arbitrary dimensions and numbers of photons using linear optical circuits described by Fourier transform matrices, and how universal linear optical quantum computing can be performed in arbitrary dimensions by combining the results with recent schemes for qudit Bell measurements.