Related papers: Compactifying linear optical unitaries using multi…
In 1994, Reck et al. showed how to realize any unitary transformation on a single photon using a product of beamsplitters and phaseshifters. Here we show that any single beamsplitter that nontrivially mixes two modes, also densely generates…
Linear optical operations are fundamental and significant for both quantum mechanics and classical technologies. We demonstrate a non-cascaded approach to perform arbitrary unitary and non-unitary linear operations for N-dimensional…
Any lossless transformation on $n_{s}$ spatial and $n_{p}$ internal modes of light can be described by an $n_{s}n_{p}\times n_{s}n_{p}$ unitary matrix, but there is no known procedure to effect an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$…
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…
Optical computing is emerging as a promising platform for energy-efficient, high-throughput hardware in deep learning. A key challenge lies in the realization of optical matrix-vector multiplication, which often requires $O(N^2)$ phase…
Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical…
Decomposing complex unitary evolution into a series of constituent components is a cornerstone of practical quantum information processing. While the decompostion of an $n\times n$ unitary into a series of $2\times2$ subunitaries is well…
Optical neural networks (ONNs) based on programmable photonic integrated circuits (PICs) offer a promising route toward low-latency and energy-efficient deep learning. However, conventional photonic implementations of matrix-vector…
Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…
All existing optical quantum walk approaches are based on the use of beamsplitters and multiple paths to explore the multitude of unitary transformations of quantum amplitudes in a Hilbert space. The beamsplitter is naturally a…
A beam splitter (BS) is one of the most critical building blocks in optical systems. Despite various attempts of flat-type BSs to miniaturize the conventional cube BS reported, it remains a challenge to realize an ultrathin optical BS with…
Using symmetry considerations, we derive a unitary scattering matrix for a three-port optical Y-coupler or Y-branch. The result is shown to be unique up to external phase shifts. Unlike traditional passive linear-optical one-way splitters,…
Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities to implement reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh…
The method of multidimensional SUSY Quantum Mechanics is applied to the investigation of supersymmetrical N-particle systems on a line for the case of separable center-of-mass motion. New decompositions of the superhamiltonian into…
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.…
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…
The concept of directionally unbiased optical multiports is introduced, in which photons may reflect back out the input direction. A linear-optical implementation is described, and the simplest three-port version studied. Symmetry arguments…
Multiport interferometers based on integrated beamsplitter meshes are widely used in photonic technologies. While the rectangular mesh is favored for its compactness and uniformity, its geometry resists conventional self-configuration…
Beam splitters (BSs) and optical parametric amplifiers (OPAs) can be described using Lie groups $SU(2)$ and $SU(1,1)$. Here, we show that the dynamical trajectories of these devices are connected via a Wick rotation on their respective…
We demonstrate a method for general linear optical networks that allows one to factorize any SU($n$) matrix in terms of two SU($n-1)$ blocks coupled by an SU(2) entangling beam splitter. The process can be recursively continued in an…