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  • Open Access

Low-depth two-unitary design of programmable photonic circuits

S. A. Fldzhyan1, M. Yu. Saygin2,1,*, and S. S. Straupe2,1

  • 1Faculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow 119991, Russia
  • 2Sber Quantum Technology Center, Kutuzovski prospect 32, Moscow 121170, Russia

  • *Contact author: saygin@physics.msu.ru
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Phys. Rev. Research 8, 013021 – Published 12 January, 2026

DOI: https://doi.org/10.1103/9fg1-fdfl

Abstract

The development of large-scale, programmable photonic circuits capable of performing generic matrix-vector multiplication is essential for both classical and quantum information processing. However, this goal is hindered by high losses, hardware errors, and difficulties in programmability. We propose an enhanced architecture for programmable photonic circuits that minimizes circuit depth and offers analytical programmability, properties that have not been simultaneously achieved in previous circuit designs. Our proposal exploits a previously overlooked representation of general nonunitary matrices as sums of two unitaries. Furthermore, similar to the traditional singular value decomposition-based circuits, the circuits in our unitary-sum-based architecture inherit the advantages of the constituent unitary circuits. Overall, our proposal provides a significantly improved solution for matrix-vector multiplication compared to the established approaches.

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Phys. Rev. Research 8, 013021– Published 12 January, 2026
  • Received 7 July 2025
  • Accepted 19 December 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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