Related papers: Simple heuristics for efficient parallel tensor co…
Distributed network optimization algorithms, such as minimum spanning tree, minimum cut, and shortest path, are an active research area in distributed computing. This paper presents a fast distributed algorithm for such problems in the…
We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed…
Graph neural networks (GNNs) have emerged as a promising direction. Training large-scale graphs that relies on distributed computing power poses new challenges. Existing distributed GNN systems leverage data parallelism by partitioning the…
TensorNetwork is an open source library for implementing tensor network algorithms. Tensor networks are sparse data structures originally designed for simulating quantum many-body physics, but are currently also applied in a number of other…
Executing quantum algorithms over distributed quantum systems requires quantum circuits to be divided into sub-circuits which communicate via entanglement-based teleportation. Naively mapping circuits to qubits over multiple quantum…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
In Nature Machine Intelligence 4, 367 (2022), Schuetz et al provide a scheme to employ graph neural networks (GNN) as a heuristic to solve a variety of classical, NP-hard combinatorial optimization problems. It describes how the network is…
In this paper, we describe efficient MapReduce simulations of parallel algorithms specified in the BSP and PRAM models. We also provide some applications of these simulation results to problems in parallel computational geometry for the…
We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and…
Recurrent neural networks (RNNs) have shown outstanding performance on processing sequence data. However, they suffer from long training time, which demands parallel implementations of the training procedure. Parallelization of the training…
Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…
This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information, designed for advanced undergraduate and graduate-level readers. In Part I, foundational topics…
We propose a parallel graph-based data clustering algorithm using CUDA GPU, based on exact clustering of the minimum spanning tree in terms of a minimum isoperimetric criteria. We also provide a comparative performance analysis of our…
We present a parallel algorithm for computing the treewidth of a graph on a GPU. We implement this algorithm in OpenCL, and experimentally evaluate its performance. Our algorithm is based on an $O^*(2^{n})$-time algorithm that explores the…
Tensor networks have been an important concept and technique in many research areas, such as quantum computation and machine learning. We study the exponential complexity of contracting tensor networks on two special graph structures:…
Circuit design for quantum machine learning remains a formidable challenge. Inspired by the applications of tensor networks across different fields and their novel presence in the classical machine learning context, one proposed method to…
We parallelize several previously proposed algorithms for the minimum routing cost spanning tree problem and some related problems.
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
CNOT circuits are a common building block of general quantum circuits. The problem of synthesizing and optimizing such circuits has received a lot of attention in the quantum computing literature. This problem is especially challenging for…