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Physical Review A

Designs of linear optical interferometers with minimal depth and component count

Timothée Goubault de Brugière, Rawad Mezher, Sebastian G. Currie, Shane Mansfield

Published Dec 24, 2025• 1 citation
Publisher
DOI
10.1103/llc6-g2f9

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Abstract We introduce procedures for decomposing N × N unitary matrices into smaller M × M unitary matrices. Our procedures enable designing modular and optimal architectures for implementing arbitrary discrete unitary transformations on light. Such architectures rely on systematically combining the M -mode linear optical interferometers together to implement a given N -mode transformation. Thus this work enables the implementation of large linear optical transformations using smaller modules that act on the spatial or the internal degrees of freedom of light such as polarization, time or orbital angular momentum. The architectures lead to a rectangular gate structure, which is optimal in the sense that realizing arbitrary transformations on these architectures needs a minimal number of optical elements and minimal circuit depth. Moreover, the rectangular structure ensures that each of the different optical modes incurs balanced optical losses, so the architectures promise substantially enhanced process fidelities as compared to existing schemes.
A crucial challenge to the scaling up of linear optical interferometers is the presence of defective optical components resulting from inevitable imperfections in fabrication and packaging. This work presents a method for circumventing such defective components including lossy modes and unresponsive phase shifters and beam-splitters. The method allows for using universal linear optical interferometers with such defects as smaller universal interferometers. The method presented here tolerates remarkably high defect rates in constructing linear optical interferometers, thus bringing closer to reality the possibility of obtaining quantum advantage with linear optics.