Complexity-energy trade-off in programmable unitary interferometers

Coherent multiport interferometers are a promising approach to realize matrix multiplication in integrated photonics. However, most known architectures - such as MZI and beamsplitter meshes, as well as more general interferometers - suffer from complicated procedures for mapping the matrix elements of the desired transformation to specific phaseshifts in the device. We point out that the high programming complexity is intrinsic, rather than accidental. At the same time, we argue that interferometers admitting efficient programming algorithms in general yield a much lower useful output energy, which ultimately limits their accuracy and energy efficiency.