Any unitary matrix can be approximately decomposed into N alternating layers of diagonal phases and a fixed tridiagonal lattice propagator, with a formal proof of finite-layer universality and numerical evidence that exactly N layers suffice.
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Universality of Photonic Interlacing Architectures for Learning Discrete Linear Unitaries
Any unitary matrix can be approximately decomposed into N alternating layers of diagonal phases and a fixed tridiagonal lattice propagator, with a formal proof of finite-layer universality and numerical evidence that exactly N layers suffice.