Self-Configuration and Error Correction in Linear Photonic Circuits

Component errors prevent linear photonic circuits from being scaled to large sizes. These errors can be compensated by programming the components in an order corresponding to nulling operations on a target matrix X through Givens rotations X→T†X, X→XT†. Nulling is implemented on hardware through measurements with feedback, in a way that builds up the target matrix even in the presence of hardware errors. This programming works with unknown errors and without internal sources or detectors in the circuit. Modifying the photonic circuit architecture can reduce the effect of errors still further, in some cases even rendering the hardware asymptotically perfect in the large-size limit. These modifications include adding a third directional coupler or crossing after each Mach-Zehnder interferometer in the circuit and a photonic implementation of the generalized FFT fractal. The configured photonic circuit can be used for machine learning, quantum photonics, prototyping, optical switching/multicast networks, microwave photonics, or signal processing.