Advanced Photonics Research

Fidelity Restorable Universal Linear Optics

Apostolos Tsakyridis, George Giamougiannis, Angelina R. Totovic, Nikos Pleros

Published Jun 19, 2022• 13 citations

Abstract

Universal multiport interferometers that can be programmed to perform any unitary or linear transformation turn into an important building block for both classical and quantum photonics. These interferometers typically utilize the mathematical framework of U(2) unitary matrix decomposition techniques and comprise a mesh of 2 × 2 beam splitters and phase shifters. All of them are, however, inherently fidelity limited as their U(2)‐based deployment approach leads to imbalanced path losses without supporting any fidelity restoration mechanism. Herein, a novel Universal Generalized Mach–Zehnder Interferometer (UGMZI) architecture is presented that migrates from U(2) decomposition techniques and adopts a recursive U(N) decomposition, exploiting cascaded size‐augmenting N N beam splitters and phase shifters. The design can natively support fidelity restoration and safeguard absolute fidelity, while outperforming the state‐of‐the‐art designs also with respect to phase‐error‐induced fidelity performance properties. Finally, it is demonstrated that its fidelity restoration properties turn the design into the optimal architecture for constructing any real/complex‐valued matrix via the singular value decomposition (SVD) scheme.

DOI: 10.1002/adpr.202200001

Related papers

Optimal design for universal multiport interferometers

William R. Clements, Peter C. Humphreys, Benjamin J. Metcalf +2 more

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.

arXiv:1603.08788OpticaDec 2, 20161,218 citations

A Coherent Photonic Crossbar for Scalable Universal Linear Optics

George Giamougiannis, Apostolos Tsakyridis, Yangjin Ma +4 more

We demonstrate a novel interferometric coherent photonic crossbar architecture (Xbar) that can realize any tensor operator and allows for total loss-induced fidelity restoration, offering at the same time significant dimension scalability credentials compared to respective state-of-the-art solutions. The proposed Xbar layout demarcates from the prevalent photonic schemes that rely on the implementation of intended matrices factorized via the Singular Value Decomposition (SVD); instead, it harnesses the power of interference within a novel design where each matrix element can be mapped by one-to-one correspondence to a single, designated Xbar node, bringing down the number of programming steps to only one. In this paper, we present the theoretical foundations of the Xbar, proving that its insertion losses do not scale with the node losses as opposed to the exponential scaling witnessed by the SVD based counterparts. This leads to a matrix design with significantly lower overall insertion losses and improved scalability potential compared to SVD-based schemes, allowing for the employment of alternative node technologies with lower energy consumption and higher operational speed credentials. Finally, we theoretically validate that the proposed Xbar architecture is the first linear operator that supports fidelity restoration, outperforming SVD schemes in loss- and phase-error fidelity performance.

arXiv:2208.12033Journal of Lightwave TechnologyJan 6, 202360 citations

Further compactifying linear optical unitaries

B. A. Bell, I. A. Walmsley

Quantum integrated photonics requires large-scale linear optical circuitry, and for many applications, it is desirable to have a universally programmable circuit, able to implement an arbitrary unitary transformation on a number of modes. This has been achieved using the Reck scheme, consisting of a network of Mach–Zehnder interferometers containing a variable phase shifter in one path as well as an external phase shifter after each Mach–Zehnder. It subsequently became apparent that with symmetric Mach–Zehnders containing a phase shifter in both paths, the external phase shifters are redundant, resulting in a more compact circuit. The rectangular Clements scheme improves on the Reck scheme in terms of circuit depth, but it has been thought that an external phase-shifter was necessary after each Mach–Zehnder. Here, we show that the Clements scheme can be realized using symmetric Mach–Zehnders, requiring only a small number of external phase-shifters that do not contribute to the depth of the circuit. This will result in a significant saving in the length of these devices, allowing more complex circuits to fit onto a photonic chip, and reducing the propagation losses associated with these circuits. We also discuss how similar savings can be made to alternative schemes, which have robustness to imbalanced beam-splitters.

arXiv:2104.07561APL PhotonicsJul 1, 202146 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:1912.04721Dec 10, 20195 citations

Near-optimal decomposition of unitary matrices using phase masks and the discrete Fourier transform

Vincent Girouard, Nicolás Quesada

Universal multiport interferometers (UMIs) have emerged as a key tool for performing arbitrary linear transformations on optical modes, enabling precise control over the state of light in essential applications of classical and quantum information processing such as neural networks and boson sampling. While UMI architectures based on Mach–Zehnder interferometer networks are well established, alternative approaches that involve interleaving fixed multichannel mixing layers and phase masks have recently gained interest due to their high robustness to losses and fabrication errors. However, these approaches currently lack optimal analytical methods to compute design parameters with a low optical depth. In this work, we introduce a constructive decomposition of unitary matrices using a sequence of 2 N +5 phase masks interleaved with 2 N +4 discrete Fourier transform matrices. This decomposition can be leveraged to design universal interferometers based on phase masks and multimode interference couplers, implementing a discrete Fourier transform, offering an analytical alternative to conventional numerical-optimization-based designs and reducing by a factor of 3 the previous best-known analytical methods.

arXiv:2508.20010Journal of the Optical Society of America BDec 3, 20256 citations

Recurrent multiport interferometers for fault-tolerant programmable photonics

Mihai Crisan, David A. Carpenter, Shamsul Arafin

Universal linear programmable photonic circuits, composed of an array of Mach-Zehnder interferometers (MZIs), are fidelity-limited devices and are prohibitively difficult to scale. To address these limitations, we propose a compact and non-feedforward recurrent MZI topology wherein light can propagate in both directions. Our recurrent mesh achieves O ( N ) scaling by building imperfect beamsplitters in series to build perfect transformations. We theoretically examine the error tolerance of our proposed recurrent interferometer under imperfect mesh parameters. Our numerical results indicate that our proposed recurrent mesh permits more than an order of magnitude reduction in implementing unitary transformations.

Optics ExpressMay 19, 20252 citations