scholarly journals Network Robustness: Detecting Topological Quantum Phases

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
Chung-Pin Chou
2003 ◽  
Vol 01 (01) ◽  
pp. 1-23 ◽  
Author(s):  
VLATKO VEDRAL

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.


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

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

Author(s):  
Mehmet Burak Şahinoğlu ◽  
Dominic Williamson ◽  
Nick Bultinck ◽  
Michaël Mariën ◽  
Jutho Haegeman ◽  
...  

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.


Science ◽  
2019 ◽  
Vol 363 (6429) ◽  
pp. 846-849 ◽  
Author(s):  
M. Kapfer ◽  
P. Roulleau ◽  
M. Santin ◽  
I. Farrer ◽  
D. A. Ritchie ◽  
...  

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.


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

2017 ◽  
Vol 119 (25) ◽  
Author(s):  
Luca Pezzè ◽  
Marco Gabbrielli ◽  
Luca Lepori ◽  
Augusto Smerzi

Sign in / Sign up

Export Citation Format

Share Document