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Designs of linear optical interferometers with minimal depth and component count

Timothée Goubault de Brugière*, Rawad Mezher, Sebastian Currie, and Shane Mansfield

  • Quandela, 7 Rue Léonard de Vinci, 91300 Massy, France

  • *Contact author: timothee.goubault@quandela.com
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Phys. Rev. A 113, 033512 – Published 9 March, 2026

DOI: https://doi.org/10.1103/llc6-g2f9

Abstract

We adapt an algorithm for cnot circuits synthesis based on the Bruhat decomposition to the design of linear optical circuits with Mach-Zehnder interferometers. The synthesis algorithm reduces to designing sorting networks with nearest neighbor swapping operations as elementary gates. We recover previous designs from the literature with the additional property that the compiler can always decide whether a unitary can be implemented on a given interferometer and, if so, returns the shallowest possible implementation. We also show natural extensions of our framework for boson sampling experiments and for the coupling of multiple integrated interferometers to design larger linear optical systems. In both cases, the designs are optimal in terms of the number of optical components. Finally, we propose a greedy design which exploits the arbitrary-but-fixed coupling of separate integrated interferometers to perform shallow boson sampling. We discuss the optimal interferometer dimensions to maximize the transmission. Beyond boson sampling, our developed framework allows a resource-favorable implementation of any nonadaptive linear optical quantum algorithm, by providing the shallowest possible interferometer for implementing this algorithm.

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Outline

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Phys. Rev. A 113, 033512– Published 9 March, 2026
  • Received 12 June 2025
  • Accepted 24 December 2025
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