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 …

Methods for simulating string-net states and anyons on a digital quantum computer

YJ Liu, K Shtengel, A Smith, F Pollmann - PRX Quantum, 2022 - APS
The finding of physical realizations of topologically ordered states in experimental settings,
from condensed matter to artificial quantum systems, has been the main challenge en route …

Topological entanglement Rényi entropy and reduced density matrix structure

ST Flammia, A Hamma, TL Hughes, XG Wen - Physical review letters, 2009 - APS
We generalize the topological entanglement entropy to a family of topological Rényi
entropies parametrized by a parameter α, in an attempt to find new invariants for …

An invitation to topological orders and category theory

L Kong, ZH Zhang - ar** between Morita-equivalent string-net states with a constant depth quantum circuit
L Lootens, B Vancraeynest-De Cuiper, N Schuch… - Physical Review B, 2022 - APS
We construct a constant depth quantum circuit that maps between Morita-equivalent string-
net models. Due to its constant depth and unitarity, the circuit cannot alter the topological …

Topological phases from higher gauge symmetry in dimensions

A Bullivant, M Calçada, Z Kádár, P Martin, JF Martins - Physical Review B, 2017 - APS
We propose an exactly solvable Hamiltonian for topological phases in 3+ 1 dimensions
utilizing ideas from higher lattice gauge theory, where the gauge symmetry is given by a …

Kitaev lattice models as a Hopf algebra gauge theory

C Meusburger - Communications in Mathematical Physics, 2017 - Springer
We prove that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is
equivalent to the combinatorial quantisation of Chern–Simons theory for the Drinfeld double …