Photonic interlacing architectures for learning discrete linear unitaries
M. Markowitz, Mohammad‐Ali Miri, Alexey Vital'evich Ovchinnikov, Kevin Zelaya · Physical Review Research · 2025
Recent investigations suggest that the discrete linear unitary group U ( N ) can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical justifications, no formal proof has been provided. Here, we show that elements of U ( N ) can be decomposed into a sequence of N -parameter phases alternating with one-parameter propagators of a lattice Hamiltonian. The proof is based on building a Lie group by alternating these two operators and showing its completeness to represent U ( N ) for a finite number of layers. This is numerically verified by using Haar random matrices as targets, showing a convergence for exactly N layers. As a specific application, we propose an integrated all-optical logic gate device that performs OR, NAND, XOR, and XAND tasks within a lossless and passive optical circuit design.