Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1603.08788 · Optica

Optimal design for universal multiport interferometers

William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf, W. Steven Kolthammer, Ian A. Walmsley

Published Dec 2, 2016• 1,218 citations
arXivHTMLPDF

Abstract

Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)PRLTAO0031-900710.1103/PhysRevLett.73.58]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.

DOI
10.1364/optica.3.001460

Related papers

Arbitrary optical wave evolution with Fourier transforms and phase masks

Víctor López-Pastor, Jeff S. Lundeen, Florian Marquardt

A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)10.1103/PhysRevLett.73.58], it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a deterministic algorithm that can find an exact and efficient implementation of any unitary transformation, using only Fourier transforms and phase masks. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from some of the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.

Optics Express•Oct 20, 2021•45 citations

Arbitrary optical wave evolution with Fourier transforms and phase masks

Víctor J. López-Pastor, Jeff S. Lundeen, Florian Marquardt

A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a constructive proof that it is possible to realize a multiport universal interferometer on N modes with a succession of 6N Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore, we provide an algorithm to find the correct succesion of Fourier transforms and phase masks to realize a given arbitrary unitary transformation. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.

arXiv:1912.04721•Dec 10, 2019•5 citations

NUMERICAL ALGORITHM FOR FINDING OPTIMAL EXPERIMENTAL SETUP FOR ARBITRARY UNITARY OPERATOR

Sushovit Adhikari, Jonathan P. Dowling

Universal multiport interferometers to implement any linear transformation are emerging as a powerful tool for quantum optics. These experimental devices are usually made from an array of beam splitters and phase shifters. Reck et al [3], provided the first algorithmic proof for experimentally realizing any arbitrary discrete unitary operator. Thus, it was made possible to measure any observable corresponding to any discrete Hermitian operator. Our work extends this idea and tries to find the best optimal experimental design for a given unitary operator. We have developed a numerical algorithm which gives an experimental design with the least number of beam splitters for a given unitary operator.

Frontiers in Optics•Jan 1, 2016•0 citations

Universal linear manipulation via routing and projective measurements

Alessio Baldazzi, Sonia Mazzucchi, Lorenzo Pavesi

Multiport interferometers with $N$ ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with $N$ components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.

quant-pharXiv:2608.05003•Aug 6, 2026•0 citations

Multiport universal unitary interferometer design

I. V. Kondratyev, I. V. Dyakonov, M. Yu. Saygin +2 more

Linear optics is a promising physical architecture for the implementation of the quantum computing devices. The key element of the linear optical quantum computer is an optical circuit realizing the sequence of transformations defined by the required quantum algorithm. The most prominent approach is the reconfigurable integrated photonics which allows to miniaturize standard optical setups on the chosen integrated photonic platform. In this paper, we propose a universal linear-optical circuit design comprised of the series of multiport beamsplitters followed by the phaseshifting elements. The proposed unitary composer device can be straightforwardly implemented using standard integrated photonic technologies. We provide guidelines for appropriate multiport beamsplitter fabrication using integrated waveguide lattices. To exemplify the performance of the composer we provide the six-mode CNOT linear optical gate circuit design fitted to described interferometric circuit.

AIP conference proceedings•Jan 1, 2020•1 citation

Universal multi-port interferometers with minimal optical depth

Luciano Pereira, Alejandro J. Rojas, Gustavo Cañas +3 more

Universal multi-port interferometers that can be reconfigured to implement any unitary operation are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Recently, Saygin et al. [Phys. Rev. Lett. 124, 010501 (2020)] have presented numerical evidence that an extremely compact arrangement consisting in $d$ layers of $d$-dimensional Fourier transforms and $d+1$ layers of configurable phase shifters might be universal in any dimension $d$. Here, we first present counterexamples to this statement. We show that for $d=3$ and $4$, around 5% of the unitary matrices from a Haar-uniform distribution cannot be recovered with high fidelity using Saygin et al.'s scheme. We also identify a family of unitary matrices with elements that cannot be recovered with high fidelity for any $5\leq d \leq 10$. Secondly, we present numerical evidence that universality is recovered in all dimensions by adding a Fourier transformation and a layer of phase shifters, which preserves the compactness of the scheme and its robustness against imperfections.

•Feb 4, 2020•5 citations
Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)PRLTAO0031-900710.1103/PhysRevLett.73.58]. We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design requires half the optical depth of the Reck design and is significantly more robust to optical losses.
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. [Phys. Rev. Lett.73, 58 (1994)10.1103/PhysRevLett.73.58], it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a deterministic algorithm that can find an exact and efficient implementation of any unitary transformation, using only Fourier transforms and phase masks. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from some of the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.
A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. it was shown how to build such multiport universal interferometers with a mesh of beam splitters and phase shifters, and this design became the basis for most experimental implementations in the last decades. However, the design of Reck et al. is difficult to scale up to a large number of modes, which would be required for many applications. Here we present a constructive proof that it is possible to realize a multiport universal interferometer on N modes with a succession of 6N Fourier transforms and 6N+1 phase masks, for any even integer N. Furthermore, we provide an algorithm to find the correct succesion of Fourier transforms and phase masks to realize a given arbitrary unitary transformation. Since Fourier transforms and phase masks are routinely implemented in several optical setups and they do not suffer from the scalability issues associated with building extensive meshes of beam splitters, we believe that our design can be useful for many applications in photonics.
Universal multiport interferometers to implement any linear transformation are emerging as a powerful tool for quantum optics. These experimental devices are usually made from an array of beam splitters and phase shifters. Reck et al [3], provided the first algorithmic proof for experimentally realizing any arbitrary discrete unitary operator. Thus, it was made possible to measure any observable corresponding to any discrete Hermitian operator. Our work extends this idea and tries to find the best optimal experimental design for a given unitary operator. We have developed a numerical algorithm which gives an experimental design with the least number of beam splitters for a given unitary operator.
Multiport interferometers with NNN ports are basic devices in both classical and quantum photonics. Ideally, they implement a linear unitary transformation between the input and output electric field vectors with NNN components, each associated with a spatial mode of classical coherent light or a single photon. Standard designs for a fully reconfigurable universal multiport interferometer are given by the Reck or the Clements schemes. In this work, we introduce routing schemes to implement a generic unitary transformation on classical coherent light or single photons using linear or tree geometries via multiple projective measurements on a single detector with the minimum number of components. Then, we generalize this result to the case of any multi-photon state for scattershot boson sampling experiments with multi-routing schemes. Finally, we test the robustness of routing schemes compared to universal schemes with respect to losses and phase noise.
Linear optics is a promising physical architecture for the implementation of the quantum computing devices. The key element of the linear optical quantum computer is an optical circuit realizing the sequence of transformations defined by the required quantum algorithm. The most prominent approach is the reconfigurable integrated photonics which allows to miniaturize standard optical setups on the chosen integrated photonic platform. In this paper, we propose a universal linear-optical circuit design comprised of the series of multiport beamsplitters followed by the phaseshifting elements. The proposed unitary composer device can be straightforwardly implemented using standard integrated photonic technologies. We provide guidelines for appropriate multiport beamsplitter fabrication using integrated waveguide lattices. To exemplify the performance of the composer we provide the six-mode CNOT linear optical gate circuit design fitted to described interferometric circuit.
Universal multi-port interferometers that can be reconfigured to implement any unitary operation are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Recently, Saygin et al. [Phys. Rev. Lett. 124, 010501 (2020)] have presented numerical evidence that an extremely compact arrangement consisting in ddd layers of ddd-dimensional Fourier transforms and d+1d+1d+1 layers of configurable phase shifters might be universal in any dimension ddd. Here, we first present counterexamples to this statement. We show that for d=3d=3d=3 and 444, around 5% of the unitary matrices from a Haar-uniform distribution cannot be recovered with high fidelity using Saygin et al.'s scheme. We also identify a family of unitary matrices with elements that cannot be recovered with high fidelity for any 5≤d≤105\leq d \leq 105≤d≤10. Secondly, we present numerical evidence that universality is recovered in all dimensions by adding a Fourier transformation and a layer of phase shifters, which preserves the compactness of the scheme and its robustness against imperfections.