Multipartite Entanglement Routing as a Hypergraph Immersion Problem

• URL: http://arxiv.org/abs/2406.13452v2
• Date: Thu, 19 Dec 2024 08:47:00 GMT
• Title: Multipartite Entanglement Routing as a Hypergraph Immersion Problem
• Authors: Yu Tian, Yuefei Liu, Xiangyi Meng,
• Abstract summary: Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs)<n>Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing.<n>Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs.
• Score: 4.3301675903966625
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Multipartite entanglement, linking multiple nodes simultaneously, is a higher-order correlation that offers advantages over pairwise connections in quantum networks (QNs). Creating reliable, large-scale multipartite entanglement requires entanglement routing, a process that combines local, short-distance connections into a long-distance connection, which can be considered as a transformation of network topology. Here, we address the question of whether a QN can be topologically transformed into another via entanglement routing. Our key result is an exact mapping from multipartite entanglement routing to Nash-Williams's graph immersion problem, extended to hypergraphs. This generalized hypergraph immersion problem introduces a partial order between QN topologies, permitting certain topological transformations while precluding others, offering discerning insights into the design and manipulation of higher-order network topologies in QNs.

Related papers

• Entanglement-Based Artificial Topology: Neighboring Remote Network Nodes [7.53305437064932]
  Entanglement is unanimously recognized as the key communication resource of the Quantum Internet. We show that multipartite entanglement allows to generate an inter-QLAN artificial topology, by means of local operations only. Our contribution aims at providing the network engineering community with a hands-on guideline towards the concept of artificial topology and artificial neighborhood.
  arXiv  Detail & Related papers  (2024-04-24T20:58:50Z)
• Hierarchical Multi-Marginal Optimal Transport for Network Alignment [52.206006379563306]
  Multi-network alignment is an essential prerequisite for joint learning on multiple networks. We propose a hierarchical multi-marginal optimal transport framework named HOT for multi-network alignment. Our proposed HOT achieves significant improvements over the state-of-the-art in both effectiveness and scalability.
  arXiv  Detail & Related papers  (2023-10-06T02:35:35Z)
• On the Bipartite Entanglement Capacity of Quantum Networks [9.377912974064227]
  We consider multi-path entanglement distribution to a pair of nodes in a quantum network consisting of devices with non-deterministic entanglement swapping capabilities. We propose a mixed-integer quadratically constrained program (MIQCP) to solve this flow problem. We then compute the overall network capacity, defined as the maximum number of EPR states distributed to users per time unit.
  arXiv  Detail & Related papers  (2023-07-10T10:58:02Z)
• Learning to Identify Graphs from Node Trajectories in Multi-Robot Networks [15.36505600407192]
  We propose a learning-based approach that efficiently uncovers graph topologies with global convergence guarantees. We demonstrate the effectiveness of our approach in identifying graphs in multi-robot formation and flocking tasks.
  arXiv  Detail & Related papers  (2023-07-10T07:09:12Z)
• QNEAT: Natural Evolution of Variational Quantum Circuit Architecture [95.29334926638462]
  We focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks. Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture. We propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC.
  arXiv  Detail & Related papers  (2023-04-14T08:03:20Z)
• Multi-User Entanglement Distribution in Quantum Networks Using Multipath Routing [55.2480439325792]
  We propose three protocols that increase the entanglement rate of multi-user applications by leveraging multipath routing. The protocols are evaluated on quantum networks with NISQ constraints, including limited quantum memories and probabilistic entanglement generation.
  arXiv  Detail & Related papers  (2023-03-06T18:06:00Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Scaling Network Topologies for Multi-User Entanglement Distribution [0.0]
  Future quantum internet relies on large-scale entanglement distribution. Quantum decoherence is a significant obstacle in large-scale networks, which otherwise perform better with multiple paths between the source and destination. We propose a new topology, connected tree, with a significant amount of redundant edges to support multi-path routing of entangled pairs.
  arXiv  Detail & Related papers  (2022-12-06T10:48:08Z)
• Quantum Federated Learning with Entanglement Controlled Circuits and Superposition Coding [44.89303833148191]
  We develop a depth-controllable architecture of entangled slimmable quantum neural networks (eSQNNs) We propose an entangled slimmable QFL (eSQFL) that communicates the superposition-coded parameters of eS-QNNs. In an image classification task, extensive simulations corroborate the effectiveness of eSQFL.
  arXiv  Detail & Related papers  (2022-12-04T03:18:03Z)
• QuanGCN: Noise-Adaptive Training for Robust Quantum Graph Convolutional Networks [124.7972093110732]
  We propose quantum graph convolutional networks (QuanGCN), which learns the local message passing among nodes with the sequence of crossing-gate quantum operations. To mitigate the inherent noises from modern quantum devices, we apply sparse constraint to sparsify the nodes' connections. Our QuanGCN is functionally comparable or even superior than the classical algorithms on several benchmark graph datasets.
  arXiv  Detail & Related papers  (2022-11-09T21:43:16Z)
• Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era [0.0]
  We provide a systematic approach to tackle with arbitrary quantum networks in the NISQ era. One application of our method is to witness the progress of essential elements in quantum networks.
  arXiv  Detail & Related papers  (2022-10-25T03:36:02Z)
• Power and limitations of single-qubit native quantum neural networks [5.526775342940154]
  Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. We formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks.
  arXiv  Detail & Related papers  (2022-05-16T17:58:27Z)
• Deep Architecture Connectivity Matters for Its Convergence: A Fine-Grained Analysis [94.64007376939735]
  We theoretically characterize the impact of connectivity patterns on the convergence of deep neural networks (DNNs) under gradient descent training. We show that by a simple filtration on "unpromising" connectivity patterns, we can trim down the number of models to evaluate.
  arXiv  Detail & Related papers  (2022-05-11T17:43:54Z)
• VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization [70.8567058758375]
  VQ-GNN is a universal framework to scale up any convolution-based GNNs using Vector Quantization (VQ) without compromising the performance. Our framework avoids the "neighbor explosion" problem of GNNs using quantized representations combined with a low-rank version of the graph convolution matrix.
  arXiv  Detail & Related papers  (2021-10-27T11:48:50Z)
• QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks [71.14713348443465]
  We introduce a trainable quantum tensor network (QTN) for quantum embedding on a variational quantum circuit (VQC) QTN enables an end-to-end parametric model pipeline, namely QTN-VQC, from the generation of quantum embedding to the output measurement. Our experiments on the MNIST dataset demonstrate the advantages of QTN for quantum embedding over other quantum embedding approaches.
  arXiv  Detail & Related papers  (2021-10-06T14:44:51Z)
• Optimized Quantum Networks [68.8204255655161]
  Quantum networks offer the possibility to generate different kinds of entanglement prior to network requests. We utilize this to design entanglement-based quantum networks tailored to their desired functionality.
  arXiv  Detail & Related papers  (2021-07-21T18:00:07Z)
• Cost vector analysis & multi-path entanglement routing in quantum networks [0.0]
  We present a framework for analysing quantum routing protocols that we call the textitcost-vector formalism. We develop rudimentary greedy algorithms for routing in this framework and test them over a variety of toy networking scenarios. Our results indicate that congestion in quantum networks does not improve significantly when more nodes (computers) are added. Rather, we find that congestion is all but eliminated by waiting a small amount of time.
  arXiv  Detail & Related papers  (2021-05-02T08:26:29Z)
• Graph Picture of Linear Quantum Networks and Entanglement [6.471031681646444]
  Linear quantum networks (LQNs) exploit the indistinguishability to generate various multipartite entangled states. It is challenging to devise a suitable LQN that carries a specific entangled state or compute the possible entangled state in a given LQN as the particle and mode number increase. This research presents a mapping process of arbitrary LQNs to graphs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement.
  arXiv  Detail & Related papers  (2021-01-02T07:27:43Z)
• DHP: Differentiable Meta Pruning via HyperNetworks [158.69345612783198]
  This paper introduces a differentiable pruning method via hypernetworks for automatic network pruning. Latent vectors control the output channels of the convolutional layers in the backbone network and act as a handle for the pruning of the layers. Experiments are conducted on various networks for image classification, single image super-resolution, and denoising.
  arXiv  Detail & Related papers  (2020-03-30T17:59:18Z)
• Entanglement Classification via Neural Network Quantum States [58.720142291102135]
  In this paper we combine machine-learning tools and the theory of quantum entanglement to perform entanglement classification for multipartite qubit systems in pure states. We use a parameterisation of quantum systems using artificial neural networks in a restricted Boltzmann machine (RBM) architecture, known as Neural Network Quantum States (NNS)
  arXiv  Detail & Related papers  (2019-12-31T07:40:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.