# Tensor networks for complex quantum systems

@article{Ors2019TensorNF, title={Tensor networks for complex quantum systems}, author={Rom{\'a}n Or{\'u}s}, journal={Nature Reviews Physics}, year={2019}, pages={1-13} }

Originally developed in the context of condensed-matter physics and based on renormalization group ideas, tensor networks have been revived thanks to quantum information theory and the progress in understanding the role of entanglement in quantum many-body systems. Moreover, tensor network states have turned out to play a key role in other scientific disciplines. In this context, here I provide an overview of the basic concepts and key developments in the field. I briefly discuss the most…

## 183 Citations

Quantum Simulation with Hybrid Tensor Networks.

- Physics, Computer SciencePhysical review letters
- 2021

This work introduces the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions.

Breaking the Entanglement Barrier: Tensor Network Simulation of Quantum Transport.

- PhysicsPhysical review letters
- 2020

Recognizing the frequency basis of quantum transport yields a striking increase in simulation efficiency, greatly extending the attainable spatial and time scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of nonequilibrium many-body problems.

Entanglement Hamiltonian tomography in quantum simulation

- Physics
- 2020

Entanglement is the crucial ingredient of quantum many-body physics, and characterizing and quantifying entanglement in closed system dynamics of quantum simulators is an outstanding challenge in…

Loop-free tensor networks for high-energy physics

- PhysicsPhilosophical Transactions of the Royal Society A
- 2021

This presentation focuses on the application of loop-free tensor network methods to the study of high-energy physics problems and, in particular, to theStudy of lattice gauge theories where tensor networks can be applied in regimes where Monte Carlo methods are hindered by the sign problem.

Entanglement of Formation of Mixed Many-Body Quantum States via Tree Tensor Operators.

- Physics, Computer SciencePhysical review letters
- 2022

This work exploits the tree tensor operator tensor network Ansatz, a positive loopless representation for density matrices which efficiently encodes information on bipartite entanglement, enabling the upscaling of entanglements estimation.

Density-Matrix Renormalization Group for Continuous Quantum Systems

- Physics, Computer Science
- 2021

This work divides space into multiple segments and generates continuous basis functions for the many-body state in each segment and shows how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum.

Random sampling neural network for quantum many-body problems

- Physics, Computer Science
- 2020

This work proposes a general numerical method, Random Sampling Neural Networks (RSNN), to utilize the pattern recognition technique for the random sampling matrix elements of an interacting many-body system via a self-supervised learning approach.

Quantum many-body systems in thermal equilibrium

- Physics
- 2022

The thermal or equilibrium ensemble is one of the most ubiquitous states of matter. For models comprised of many locally interacting quantum particles, it describes a wide range of physical…

Symmetries in topological tensor network states: classification, construction and detection

- Mathematics
- 2019

This thesis contributes to the understanding of symmetry-enriched topological phases focusing on their descriptions in terms of tensor network states by proposing a family of gauge invariant quantities and their corresponding order parameters to detect the corresponding quantum phases, in particular their symmetry fractionalization patterns.

Many-body quantum states with exact conservation of non-Abelian and lattice symmetries through variational Monte Carlo

- Computer SciencePhysical Review B
- 2021

This work presents an ansatz where global non-abelian symmetries are inherently embedded in its structure and extends the model to incorporate lattice asymmetries as well, allowing to find the wave functions of excited states with definite quantum numbers associated to the considered symmetry without modifying the architecture of the network.

## References

SHOWING 1-10 OF 292 REFERENCES

Entanglement Continuous Unitary Transformations

- Physics
- 2016

Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a…

Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order

- Physics
- 2009

We study the renormalization group flow of the Lagrangian for statistical and quantum systems by representing their path integral in terms of a tensor network. Using a tensor-entanglement-filtering…

Neural-Network Quantum States, String-Bond States, and Chiral Topological States

- Physics, Computer Science
- 2018

The results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of String-Bond States as a tool in more traditional machine-learning applications.

Fermionic multiscale entanglement renormalization ansatz

- Physics
- 2009

In a recent contribution [P. Corboz, G. Evenbly, F. Verstraete, and G. Vidal, arXiv:0904.4151 (unpublished)] entanglement renormalization was generalized to fermionic lattice systems in two spatial…

Tensor product methods and entanglement optimization for ab initio quantum chemistry

- Computer Science
- 2015

A pedagogical introduction to the theoretical background of this novel field of entanglement and the underlying benefits through numerical applications on a text book example are demonstrated.

Renormalization Group Flows of Hamiltonians Using Tensor Networks.

- PhysicsPhysical review letters
- 2017

It is emphasized that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of the local basis at every decimation step, a property which is crucial to overcome the area law of mutual information.

Advances on tensor network theory: symmetries, fermions, entanglement, and holography

- Physics
- 2014

This is a short review on selected theory developments on tensor network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic…