scholarly journals Network Robustness: Detecting Topological Quantum Phases

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Chung-Pin Chou
Keyword(s):  
Network Robustness ◽  
Quantum Phases ◽  
Topological Quantum

scholarly journals GEOMETRIC PHASES AND TOPOLOGICAL QUANTUM COMPUTATION

2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL
Keyword(s):  
Quantum Computation ◽  
Large Scale ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Geometric Phases ◽  
Quantum Phases ◽  
Topological Quantum ◽  
Universal Quantum ◽  
The Subject ◽  
Topological Quantum Computation

In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum computation using only geometric effects appearing in quantum phases. It is then finally discussed how this geometric way of performing quantum gates can lead to a stable, large scale, intrinsically fault-tolerant quantum computer.

scholarly journals Dynamical classification of topological quantum phases

2018 ◽  
Vol 63 (21) ◽  
pp. 1385-1391 ◽  
Author(s):  
Lin Zhang ◽  
Long Zhang ◽  
Sen Niu ◽  
Xiong-Jun Liu
Keyword(s):  
Quantum Phases ◽  
Topological Quantum

scholarly journals Geometric classification of topological quantum phases

1998 ◽  
Vol 237 (4-5) ◽  
pp. 195-200 ◽  
Author(s):  
Christopher Kohler
Keyword(s):  
Quantum Phases ◽  
Topological Quantum

scholarly journals Characterizing Topological Order with Matrix Product Operators

2021 ◽  
Author(s):  
Mehmet Burak Şahinoğlu ◽  
Dominic Williamson ◽  
Nick Bultinck ◽  
Michaël Mariën ◽  
Jutho Haegeman ◽  
...  
Keyword(s):  
Ground State ◽  
Local Order ◽  
Virtual Level ◽  
Matrix Product ◽  
Topological Phases ◽  
Topological Order ◽  
Quantum Phases ◽  
Topological Features ◽  
Topological Quantum ◽  
Tensor Network

AbstractOne of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of $${\mathsf {G}}$$ G - and twisted injectivity; the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.

scholarly journals A Josephson relation for fractionally charged anyons

Science ◽  
2019 ◽  
Vol 363 (6429) ◽  
pp. 846-849 ◽  
Author(s):  
M. Kapfer ◽  
P. Roulleau ◽  
M. Santin ◽  
I. Farrer ◽  
D. A. Ritchie ◽  
...  
Keyword(s):  
Quantum Hall ◽  
Dynamical Property ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Fractional Quantum ◽  
Time Resolved ◽  
Quantum Phases ◽  
Fractional Charge ◽  
Fractional Quantum Hall ◽  
Topological Quantum

Anyons occur in two-dimensional electron systems as excitations with fractional charge in the topologically ordered states of the fractional quantum Hall effect (FQHE). Their dynamics are of utmost importance for topological quantum phases and possible decoherence-free quantum information approaches, but observing these dynamics experimentally is challenging. Here, we report on a dynamical property of anyons: the long-predicted Josephson relation fJ = e*V/h for charges e* = e/3 and e/5, where e is the charge of the electron and h is Planck’s constant. The relation manifests itself as marked signatures in the dependence of photo-assisted shot noise (PASN) on voltage V when irradiating contacts at microwaves frequency fJ. The validation of FQHE PASN models indicates a path toward realizing time-resolved anyon sources based on levitons.

scholarly journals Fidelity in topological quantum phases of matter

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Silvano Garnerone ◽  
Damian Abasto ◽  
Stephan Haas ◽  
Paolo Zanardi
Keyword(s):  
Quantum Phases ◽  
Topological Quantum

scholarly journals Multipartite Entanglement in Topological Quantum Phases

2017 ◽  
Vol 119 (25) ◽  
Author(s):  
Luca Pezzè ◽  
Marco Gabbrielli ◽  
Luca Lepori ◽  
Augusto Smerzi
Keyword(s):  
Multipartite Entanglement ◽  
Quantum Phases ◽  
Topological Quantum
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