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  • Open Access

Photonic interlacing architectures for learning discrete linear unitaries

M. Markowitz, M.-A. Miri*, A. Ovchinnikov, and K. Zelaya

  • *Contact author: mmiri@qc.cuny.edu
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Phys. Rev. Research 7, 033205 – Published 2 September, 2025

DOI: https://doi.org/10.1103/4vth-6n7q

Abstract

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.

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Phys. Rev. Research 7, 033205– Published 2 September, 2025
  • Received 14 February 2025
  • Accepted 7 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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