Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2503.08626 · Nature Reviews Physics

Tensor networks for quantum computing

A. V. Berezutskii, Minzhao Liu, Atithi Acharya, Roman Ellerbrock, Johnnie Gray, Reza Haghshenas, Zichang He, Abid Khan, Viacheslav Kuzmin, Dmitry I. Lyakh, Danylo Lykov, Salvatore Mandrà, Christopher Mansell, Alexey A. Melnikov, Artem Melnikov, Vladimir Mironov, Dmitry I. Morozov, Florian Neukart, Alberto Nocera, Michael A. Perlin, Michael Romanovich Perelshtein, Matthew Steinberg, Ruslan Shaydulin, Benjamin Villalonga, Markus Pflitsch, Marco Pistoia, V. M. Vinokur, Yuri Alexeev

Published Jul 30, 2025• 21 citations
arXivHTMLPDF
DOI
10.1038/s42254-025-00853-1

Related papers

Tensor Networks in Quantum Neural Network Architectures

K. Meenakshi, Rakhi Chauhan, Deepshikha Bhargava

Signals and communication technology•Jan 1, 2026•0 citations

Implementation of Tensor Network Simulation TN-Sim under NWQ-Sim

Aaron C. Hoyt, Jonathan S. Bersson, Sean Garner +2 more

Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.

quant-pharXiv:2601.04422•IEEE High Performance Extreme Computing Conference•Jan 9, 2026•0 citations

Tensor Network Techniques for Quantum Computation

Mario Collura, Guglielmo Lami, Nishan Ranabhat +1 more

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. In presenting tensor networks as tools for understanding quantum complexity, this book aims to foster a deeper collaboration between the many-body physics and quantum computing communities, inviting a broader audience to engage with these recent developments.

arXiv:2503.04423•Dec 1, 2024•7 citations

TENSOR NETWORKS FOR OPEN QUANTUM SYSTEMS

Dario Tamascelli, A. Mennella, Davide Ferracin

•Jan 27, 2026•0 citations

Computations in quantum tensor networks

Thomas Huckle, Konrad Waldherr, Thomas Schulte‐Herbrüggen

arXiv:1212.5005•Linear Algebra and its Applications•Jan 27, 2012•57 citations

Vectorized Symmetric and Fermionic Tensor Network Implementations for GPU-Accelerated Variational Monte Carlo

Si-Jing Du, Johnnie Gray, Ao Chen +1 more

Variational Monte Carlo (VMC) calculations based on tensor networks (TN) have recently achieved competitive accuracy in ground-state calculations of strongly correlated spin and fermionic systems. However, existing tensor network VMC (TN-VMC) algorithms have not been formulated in a manner that can fully utilize GPU acceleration. We tackle the key missing ingredient, namely, the vectorized evaluation of tensor network amplitudes and tensor network operations. This ensures high GPU utilization by batching over computations with identical structure. In particular, we show how to achieve vectorization for the practically relevant case of abelian symmetric tensor networks (which includes fermionic tensor networks) by developing a ``flat'' tensor network formalism for block-sparse tensor representation and contraction. Using this, we construct a GPU-adapted symmetric TN-VMC workflow with batched tensor network computation. In the two-dimensional Fermi--Hubbard model, we demonstrate a GPU speedup of up to $300 \times$ over single core CPU implementations, for fermionic TN variational wavefunctions.

physics.comp-phCross-listedarXiv:2608.27861•Aug 31, 2026•0 citations
Large-scale tensor network simulations are crucial for developing robust complexity-theoretic bounds on classical quantum simulation, enabling circuit cutting approaches, and optimizing circuit compilation, all of which aid efficient quantum computation on limited quantum resources. Modern exascale high-performance computing platforms offer significant potential for advancing tensor network quantum circuit simulation capabilities. We implement TN-Sim, a tensor network simulator backend within the NWQ-Sim software package that utilizes the Tensor Algebra for Many-body Methods (TAMM) framework to support both distributed HPC-scale computations and local simulations with ITensor. To optimize the scale up in computation across multiple nodes we implement a task based parallelization scheme to demonstrate parallelized gate contraction for wide quantum circuits with many gates per layer. Through the integration of the TAMM framework with Matrix Product State (MPS) tensor network approaches, we deliver a simulation environment that can scale from local systems to HPC clusters. We demonstrate an MPS tensor network simulator running on the state-of-the-art Perlmutter (NVIDIA) supercomputer and discuss the potential portability of this software to HPC clusters such as Frontier (AMD) and Aurora (Intel). We also discuss future improvements including support for different tensor network topologies and enhanced computational efficiency.
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. In presenting tensor networks as tools for understanding quantum complexity, this book aims to foster a deeper collaboration between the many-body physics and quantum computing communities, inviting a broader audience to engage with these recent developments.
Variational Monte Carlo (VMC) calculations based on tensor networks (TN) have recently achieved competitive accuracy in ground-state calculations of strongly correlated spin and fermionic systems. However, existing tensor network VMC (TN-VMC) algorithms have not been formulated in a manner that can fully utilize GPU acceleration. We tackle the key missing ingredient, namely, the vectorized evaluation of tensor network amplitudes and tensor network operations. This ensures high GPU utilization by batching over computations with identical structure. In particular, we show how to achieve vectorization for the practically relevant case of abelian symmetric tensor networks (which includes fermionic tensor networks) by developing a ``flat'' tensor network formalism for block-sparse tensor representation and contraction. Using this, we construct a GPU-adapted symmetric TN-VMC workflow with batched tensor network computation. In the two-dimensional Fermi--Hubbard model, we demonstrate a GPU speedup of up to 300×300 \times300× over single core CPU implementations, for fermionic TN variational wavefunctions.