相关论文: Coded FFT and Its Communication Overhead
Code switching is an established technique that facilitates a universal set of FT quantum gate operations by combining two QEC codes with complementary sets of gates, which each by themselves are easy to implement fault-tolerantly. In this…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
A novel fountain coding scheme has been introduced. The scheme consists of a parallel concatenation of a MDS block code with a LRFC code, both constructed over the same field, $F_q$. The performance of the concatenated fountain coding…
The presented work provides a procedure for optimizing the communication cost of a distributed quantum circuit (DQC) in terms of the number of qubit teleportations. Because of technology limitations which do not allow large quantum…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
In distributed quantum storage, physical qubits of a code will be stored across the network. When qubits in one of the nodes are lost i.e. when the node is erased, the remaining nodes need to communicate with a new node to replace the lost…
The work here studies the communication cost for a multi-server multi-task distributed computation framework, and does so for a broad class of functions and data statistics. Considering the framework where a user seeks the computation of…
Federated learning is a widely used distributed deep learning framework that protects the privacy of each client by exchanging model parameters rather than raw data. However, federated learning suffers from high communication costs, as a…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
The Metaverse, a burgeoning collective virtual space merging augmented reality and persistent virtual worlds, necessitates advanced artificial intelligence (AI) and communication technologies to support immersive and interactive…
We study the inherent space requirements of shared storage algorithms in asynchronous fault-prone systems. Previous works use codes to achieve a better storage cost than the well-known replication approach. However, a closer look reveals…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
Erasure codes are increasingly being studied in the context of implementing atomic memory objects in large scale asynchronous distributed storage systems. When compared with the traditional replication based schemes, erasure codes have the…
By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast, stable, and simple algorithm for computing the NUDFT that costs $\mathcal{O}(N\log…
We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…
Massively parallel Fourier transforms are widely used in computational sciences, and specifically in computational fluid dynamics which involves unbounded Poisson problems. In practice the latter is usually the most time-consuming operation…
We consider the well-studied Sparse Fourier transform problem, where one aims to quickly recover an approximately Fourier $k$-sparse vector $\widehat{x} \in \mathbb{C}^{n^d}$ from observing its time domain representation $x$. In the exact…
In a large-scale and distributed matrix multiplication problem $C=A^{\intercal}B$, where $C\in\mathbb{R}^{r\times t}$, the coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may…
Adaptive Fourier decomposition (AFD, precisely 1-D AFD or Core-AFD) was originated for the goal of positive frequency representations of signals. It achieved the goal and at the same time offered fast decompositions of signals. There then…