Tensor Network Techniques for Quantum Computation

• URL: http://arxiv.org/abs/2503.04423v1
• Date: Thu, 06 Mar 2025 13:31:17 GMT
• Title: Tensor Network Techniques for Quantum Computation
• Authors: Mario Collura, Guglielmo Lami, Nishan Ranabhat, Alessandro Santini,
• Abstract summary: This book serves as an introductory yet thorough guide to tensor networks and their applications in quantum computation and quantum information.<n>In Part I, foundational topics are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Networks (TTN)<n>Part II explores practical applications of tensor networks in simulating quantum dynamics.<n>A final chapter addresses the emerging role of "quantum magic" in tensor networks.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 are covered, including tensor structures and network representations like Matrix Product States (MPS) and Tree Tensor Networks (TTN). These preliminaries provide readers with the core mathematical tools and concepts necessary for quantum physics and quantum computing applications, bridging the gap between multi-linear algebra and complex quantum systems. Part II explores practical applications of tensor networks in simulating quantum dynamics, with a particular focus on the efficiency they offer for systems of high computational complexity. Key topics include Hamiltonian dynamics, quantum annealing, open system dynamics, and optimization strategies using TN frameworks. A final chapter addresses the emerging role of "quantum magic" in tensor networks. It delves into non-stabilizer states and their contribution to quantum computational power beyond classical simulability, featuring methods such as stabilizer-enhanced MPS and the Clifford-dressed TDVP.

Related papers

• Tensor networks for quantum computing [27.077215121982192]
  We review the diverse applications of tensor networks and show that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum synthesis, quantum circuit, quantum error correction, and quantum machine learning.
  arXiv  Detail & Related papers  (2025-03-11T17:10:41Z)
• Comprehensive Survey of QML: From Data Analysis to Algorithmic Advancements [2.5686697584463025]
  Quantum Machine Learning represents a paradigm shift at the intersection of Quantum Computing and Machine Learning.<n>The field faces significant challenges, including hardware constraints, noise, and limited qubit coherence.<n>This survey aims to provide a foundational resource for advancing Quantum Machine Learning toward practical, real-world applications.
  arXiv  Detail & Related papers  (2025-01-16T13:25:49Z)
• Quantum Annealing and Tensor Networks: a Powerful Combination to Solve Optimization Problems [0.0]
  The aim of this thesis is not to compare quantum devices with tensor network algorithms.<n>We explore a potential synergy between these technologies, focusing on how two flagship algorithms might collaborate in the future.<n>This thesis outlines an approach to this problem using finite automata, which we apply to construct the MPO for our case study.
  arXiv  Detail & Related papers  (2024-12-07T09:20:20Z)
• Survey on Computational Applications of Tensor Network Simulations [0.0]
  Review aims to clarify which classes of relevant applications have been proposed for which class of tensor networks. We intend this review to be a high-level tour on tensor network applications which is easy to read by non-experts.
  arXiv  Detail & Related papers  (2024-08-09T11:46:47Z)
• A Matrix Product State Model for Simultaneous Classification and Generation [0.8192907805418583]
  Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. Here, we present a novel matrix product state (MPS) model, where the MPS functions as both a classifier and a generator. Our contributions offer insights into the mechanics of tensor network methods for generation tasks.
  arXiv  Detail & Related papers  (2024-06-25T10:23:36Z)
• Entanglement-Assisted Quantum Networks: Mechanics, Enabling Technologies, Challenges, and Research Directions [66.27337498864556]
  This paper presents a comprehensive survey of entanglement-assisted quantum networks. It provides a detailed overview of the network structure, working principles, and development stages. It also emphasizes open research directions, including architecture design, entanglement-based network issues, and standardization.
  arXiv  Detail & Related papers  (2023-07-24T02:48:22Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Quantum Phase Recognition using Quantum Tensor Networks [0.0]
  This paper examines a quantum machine learning approach based on shallow variational ansatz inspired by tensor networks for supervised learning tasks. We are able to reach $geq 98%$ test-set accuracies with both multi-scale entanglement renormalization ansatz (MERA) and tree tensor network (TTN) inspired parametrized quantum circuits.
  arXiv  Detail & Related papers  (2022-12-12T19:29:07Z)
• Quantum Federated Learning with Quantum Data [87.49715898878858]
  Quantum machine learning (QML) has emerged as a promising field that leans on the developments in quantum computing to explore large complex machine learning problems. This paper proposes the first fully quantum federated learning framework that can operate over quantum data and, thus, share the learning of quantum circuit parameters in a decentralized manner.
  arXiv  Detail & Related papers  (2021-05-30T12:19:27Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• 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.