Related papers: Native QR Factorization on Programmable Photonic M…
Programmable photonic circuits (PPCs) have garnered substantial interest in achieving deep learning accelerations and universal quantum computations. Although photonic computation using PPCs offers critical advantages, including ultrafast…
We develop two fast algorithms for Hessenberg reduction of a structured matrix $A = D + UV^H$ where $D$ is a real or unitary $n \times n$ diagonal matrix and $U, V \in\mathbb{C}^{n \times k}$. The proposed algorithm for the real case…
We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or…
Photonic integrated circuits offer a compact and stable platform for generating, manipulating, and detecting light. They are instrumental for classical and quantum applications. Imperfections stemming from fabrication constraints,…
As computing resource demands continue to escalate in the face of big data, cloud-connectivity and the internet of things, it has become imperative to develop new low-power, scalable architectures. Neuromorphic photonics, or photonic neural…
Programmable integrated photonics (PIP) has emerged as a powerful on-chip platform for optical signal processing and computing, enabling the implementation of reconfigurable N$\times$N unitary matrix transformations through meshes of…
Standard rank-revealing factorizations such as the singular value decomposition and column pivoted QR factorization are challenging to implement efficiently on a GPU. A major difficulty in this regard is the inability of standard algorithms…
Chebyshev filtered subspace iteration is a well-known algorithm for the solution of (symmetric/Hermitian) algebraic eigenproblems which has been implemented in several application codes~\cite{Kronik:2006ff, abinit:2020} or in stand alone…
Several complex tasks that arise in organizations can be simplified by mapping them into a matrix completion problem. In this paper, we address a key challenge faced by our company: predicting the efficiency of artists in rendering visual…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
Nonnegative matrix factorization is the following problem: given a nonnegative input matrix $V$ and a factorization rank $K$, compute two nonnegative matrices, $W$ with $K$ columns and $H$ with $K$ rows, such that $WH$ approximates $V$ as…
Large-scale generation of quantum entanglement between individually controllable qubits is at the core of quantum computing, communications, and sensing. Modular architectures of remotely-connected quantum technologies have been proposed…
This paper introduces fast R updating algorithms specifically designed for statistical applications, including regression, filtering, and model selection, where data structures change frequently. Although traditional QR decomposition is…
We design optimal interferometric schemes for implementation of two-qubit linear optical quantum filters diagonal in the computational basis. The filtering is realized by interference of the two photons encoding the qubits in a multiport…
The classic rank-revealing QR factorization factorizes a matrix $A$ as $AP=QR$ where $P$ permutes the columns of $A$, $Q$ is an orthogonal matrix, and $R$ is upper triangular with non-increasing diagonal entries. This is called…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
We present an interdigitated capacitor trimming technique for fine-tuning the resonance frequency of superconducting microresonators and increasing the multiplexing factor. We first measure the optical response of the array with a beam…
Programmable unitary photonic networks that interfere hundreds of modes are emerging as a key technology in energy-efficient sensing, machine learning, cryptography, and linear optical quantum computing applications. In this work, we…
Structured light, light tailored in its internal degrees of freedom, has become topical in numerous quantum and classical information processing protocols. In this work, we harness the high dimensional nature of structured light modulated…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…