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Tensor network states are capable of describing many-body systems with complex quantum entanglement, including systems with non-trivial topological order. In this paper, we study methods to calculate the topological properties of a tensor…

Strongly Correlated Electrons · Physics 2010-01-26 Brian Swingle , Xiao-Gang Wen

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we…

Quantum Physics · Physics 2024-12-04 Michael L. Wall , Aidan Reilly , John S. Van Dyke , Collin Broholm , Paraj Titum

Efficient methods to access the entanglement of a quantum many-body state, where the complexity generally scales exponentially with the system size $N$, have long a concern. Here we propose the Schmidt tensor network state (Schmidt TNS)…

Quantum Physics · Physics 2023-07-18 Peng-Fei Zhou , Ying Lu , Jia-Hao Wang , Shi-Ju Ran

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement…

Quantum Physics · Physics 2020-09-30 Matthias Christandl , Angelo Lucia , Péter Vrana , Albert H. Werner

Trial wavefunctions that can be represented by summing over locally-coupled degrees of freedom are called tensor network states (TNSs); they have seemed difficult to construct for two-dimensional topological phases that possess protected…

Mesoscale and Nanoscale Physics · Physics 2015-11-25 J. Dubail , N. Read

We introduce a method for extracting meaningful entanglement measures of tensor network states in general dimensions. Current methods require the explicit reconstruction of the density matrix, which is highly demanding, or the contraction…

Strongly Correlated Electrons · Physics 2022-07-28 Noa Feldman , Augustine Kshetrimayum , Jens Eisert , Moshe Goldstein

We propose a single-layer tensor network framework for the variational determination of ground states in two-dimensional quantum lattice models. By combining the nested tensor network method [Phys. Rev. B 96, 045128 (2017)] with the…

Strongly Correlated Electrons · Physics 2026-04-17 Hongyu Chen , Yangfeng Fu , Weiqiang Yu , Rong Yu , Z. Y. Xie

We present a scheme to perform an iterative variational optimization with infinite projected entangled-pair states (iPEPS), a tensor network ansatz for a two-dimensional wave function in the thermodynamic limit, to compute the ground state…

Strongly Correlated Electrons · Physics 2017-05-02 Philippe Corboz

We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…

Quantum Physics · Physics 2025-01-06 Wen-Yuan Liu , Si-Jing Du , Ruojing Peng , Johnnie Gray , Garnet Kin-Lic Chan

Tensor networks (TNs) enable compact representations of large tensors through shared parameters. Their use in probabilistic modeling is particularly appealing, as probabilistic tensor networks (PTNs) allow for tractable computation of…

Machine Learning · Computer Science 2025-10-02 Marawan Gamal Abdel Hameed , Guillaume Rabusseau

Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-$N$ tensor from exponential…

Strongly Correlated Electrons · Physics 2022-05-31 Hao Chen , Thomas Barthel

We construct a tensor network representation of the 3d toric code ground state that is stable to a generating set of uniform local tensor perturbations, including those that do not map to local operators on the physical Hilbert space. The…

Strongly Correlated Electrons · Physics 2021-12-30 Dominic J. Williamson , Clement Delcamp , Frank Verstraete , Norbert Schuch

Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…

General Relativity and Quantum Cosmology · Physics 2016-03-23 Alexandre Feller , Etera R. Livine

Topology inference is a powerful tool to better understand the behaviours of network systems (NSs). Different from most of prior works, this paper is dedicated to inferring the directed topology of NSs from noisy observations, where the…

Systems and Control · Electrical Eng. & Systems 2025-09-03 Qing Jiao , Yushan Li , Jianping He

Tree tensor network (TTN) provides an essential theoretical framework for the practical simulation of quantum many-body systems, where the network structure defined by the connectivity of the isometry tensors plays a crucial role in…

Statistical Mechanics · Physics 2023-01-24 Toshiya Hikihara , Hiroshi Ueda , Kouichi Okunishi , Kenji Harada , Tomotoshi Nishino

A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of…

Statistical Mechanics · Physics 2015-06-05 Shi-Ju Ran , Wei Li , Bin Xi , Zhe Zhang , Gang Su

We apply the charge pumping argument to fermionic tensor network representations of d-dimensional topological insulators (TIs) to obtain tensor network states for (d+1)-dimensional TIs. We exemplify the method by constructing a…

Strongly Correlated Electrons · Physics 2020-03-25 Anna Hackenbroich , B. Andrei Bernevig , Norbert Schuch , Nicolas Regnault

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…

Being able to describe accurately the dynamics and steady-states of driven and/or dissipative but quantum correlated lattice models is of fundamental importance in many areas of science: from quantum information to biology. An efficient…

Quantum Physics · Physics 2021-05-19 Conor Mc Keever , Marzena H. Szymańska

We propose the entanglement bipartitioning approach to design an optimal network structure of the tree-tensor-network (TTN) for quantum many-body systems. Given an exact ground-state wavefunction, we perform sequential bipartitioning of…

Quantum Physics · Physics 2023-03-02 Kouichi Okunishi , Hiroshi Ueda , Tomotoshi Nishino