Programmable unitary transformations on integrated photonics platforms are becoming a powerful tool for quantum computing, machine learning, and optical communications. A major challenge is dealing with the fabrication errors of these circuits, which can degrade performance. One common approach uses a mesh of Mach-Zehnder interferometers (MZIs) to decompose arbitrary unitary transformations into
U(2)transformations [1]. While this architecture is mathematically clear and provides an explicit method for determining the phase shifts in each MZI, it is also sensitive to fabrication errors, and ongoing research is focused on finding ways to correct these errors.
Integrated multi-port interferometers are the second step in programmable photonics. Initially conceived and designed to implement fixed linear optics unitary transformations between N input and N output ports to support mode transformations in quantum optics, the rapid development of this field and the possibility of applying these structures to other areas stimulated development of devices capable of supporting arbitrary linear transformations by suitable programming and surpassing use in square matrix transformations and unitary operators. This chapter reviews some basic concepts on unitary N×N matrices and then describes in detail the basic design principles and integrated optics implementations of triangular and rectangular designs for multi-port interferometers. It then considers more specific interferometer designs, which do not provide possible implementation of general linear transformations but are optimised for performing important operations, e.g. the Fourier transform. Lastly, it covers the linear universal component, which integrates both universal beam couplers and integrated multi-port interferometers.
Reconfigurable devices capable to implement any unitary operation with a given fidelity are crucial for photonic universal quantum computation, optical neural networks, and boson sampling. Here, we address the problems of approximating with a given infidelity any unitary operation and any pure state using multi-port interferometers, which are of current interest due to the recent availability of multi-core fiber integrated multi-port interferometers. We show that any pure state, in any dimension
d, can be prepared with infidelity
≤10−15 with
3~layers of
d-dimensional Fourier transforms and
3~layers of configurable phase shifters. In contrast, the schemes in [Phys. Rev. Lett. \textbf{73}, 58 (1994) and Optica \textbf{3}, 1460 (2016)], require optical depth
2(d−1). We also present numerical evidence that
d+1~layers of
d-dimensional Fourier transforms and
d+2~layers of configurable phase shifters can produce any unitary with infidelity
≤10−14, while the scheme in [Phys. Rev. Lett. \textbf{124}, 010501 (2020)] only achieves an infidelity in the order of
10−7 for block-diagonal unitary transformations
Unitary operations are a specific class of linear transformations that have become an essential ingredient for the realization of classical and quantum information processing. The ability of implementing any n-dimensional unitary signal transformation by using a reconfigurable optical hardware has recently led to the pioneering concept of programmable linear optical processor, whose basic building block (BB) must be correctly designed to guarantee that the whole system is able to perform n × n universal (i.e., arbitrary) unitary matrix transformations. Here, it is demonstrated that the present architectures of the BB do not fulfil the universal unitary property (at least) in 2 × 2 optical processors, limiting the number of unitary matrix transformations that may be generated. Aiming to solve this fundamental constraint, the theoretical tools required to analyze and design 2 × 2 universal unitary optical circuits and their corresponding BBs are presented. The consequences of this mathematical framework are explored, obtaining a simple route to implement different BB architectures, all of them guaranteeing a true universal unitary functionality in the resulting 2 × 2 optical processors. These findings may pave the way to revisit the design of high-dimensional unitary optical processors, unleashing the potential of programmable integrated photonics technology.
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.