Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing
interactions and correlations in many-body systems. Its vocabulary consists of qubits and …
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
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 …
from condensed matter to artificial quantum systems, has been the main challenge en route …
Topological entanglement Rényi entropy and reduced density matrix structure
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 …
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
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 …
net models. Due to its constant depth and unitarity, the circuit cannot alter the topological …
Topological phases from higher gauge symmetry in dimensions
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 …
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 …
equivalent to the combinatorial quantisation of Chern–Simons theory for the Drinfeld double …