Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

JI Cirac, D Perez-Garcia, N Schuch, F Verstraete - Reviews of Modern Physics, 2021 - APS
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …

Tensor networks for complex quantum systems

R Orús - Nature Reviews Physics, 2019 - nature.com
Originally developed in the context of condensed-matter physics and based on
renormalization group ideas, tensor networks have been revived thanks to quantum …

Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution

M Motta, C Sun, ATK Tan, MJ O'Rourke, E Ye… - Nature Physics, 2020 - nature.com
The accurate computation of Hamiltonian ground, excited and thermal states on quantum
computers stands to impact many problems in the physical and computer sciences, from …

Computational advantage of quantum random sampling

D Hangleiter, J Eisert - Reviews of Modern Physics, 2023 - APS
Quantum random sampling is the leading proposal for demonstrating a computational
advantage of quantum computers over classical computers. Recently the first large-scale …

Simulation methods for open quantum many-body systems

H Weimer, A Kshetrimayum, R Orús - Reviews of Modern Physics, 2021 - APS
Coupling a quantum many-body system to an external environment dramatically changes its
dynamics and offers novel possibilities not found in closed systems. Of special interest are …

Lattice quantum electrodynamics in (3+ 1)-dimensions at finite density with tensor networks

G Magnifico, T Felser, P Silvi, S Montangero - Nature communications, 2021 - nature.com
Gauge theories are of paramount importance in our understanding of fundamental
constituents of matter and their interactions. However, the complete characterization of their …

Neural tensor contractions and the expressive power of deep neural quantum states

O Sharir, A Shashua, G Carleo - Physical Review B, 2022 - APS
We establish a direct connection between general tensor networks and deep feed-forward
artificial neural networks. The core of our results is the construction of neural-network layers …

Time-dependent variational principle for open quantum systems with artificial neural networks

M Reh, M Schmitt, M Gärttner - Physical Review Letters, 2021 - APS
We develop a variational approach to simulating the dynamics of open quantum many-body
systems using deep autoregressive neural networks. The parameters of a compressed …

Efficient Tensor Network Ansatz for High-Dimensional Quantum Many-Body Problems

T Felser, S Notarnicola, S Montangero - Physical Review Letters, 2021 - APS
We introduce a novel tensor network structure augmenting the well-established tree tensor
network representation of a quantum many-body wave function. The new structure satisfies …

Quantum many-body systems in thermal equilibrium

ÁM Alhambra - PRX Quantum, 2023 - APS
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 …