Ising-type non-Abelian anyons are likely to occur in a number of physical systems, including quantum Hall systems, where recent experiments support their existence. In general, non-Abelian anyons may be utilized to provide a topologically error-protected medium for quantum information processing. However, the topologically protected operations that may be obtained by braiding and measuring topological charge of Ising anyons are precisely the Clifford gates, which are not computationally universal. The Clifford gate set can be made universal by supplementing it with single-qubit pi/8-phase gates. We propose a method of implementing arbitrary single-qubit phase gates for Ising anyons by running a current of anyons with interfering paths around computational anyons.Ising-type non-Abelian anyons are likely to occur in a number of physical systems, including quantum Hall systems, where recent experiments support their existence. In general, non-Abelian anyons may be utilized to provide a topologically error-protected medium for quantum information processing. However, the topologically protected operations that may be obtained by braiding and measuring topological charge of Ising anyons are precisely the Clifford gates, which are not computationally universal. The Clifford gate set can be made universal by supplementing it with single-qubit pi/8-phase gates. We propose a method of implementing arbitrary single-qubit phase gates for Ising anyons by running a current of anyons with interfering paths around computational anyons.

arXiv:0911.2691Physical Review LettersMay 7, 201067 citations

Anyons and the Fractional Quantum Hall Effect

Lecture notes in physics. M, MonographsJan 1, 19920 citations

Adiabatic Cooling with Non-Abelian Anyons

G. Gervais, Kun Yang

We show in this Letter that the ground state degeneracy associated with the presence of non-Abelian anyons can be probed by using an adiabatic cooling process based on the non-Abelian entropy. In particular, we show that when the number of such anyons is increased adiabatically at sufficiently low temperatures, the non-Abelian liquid undergoes cooling, whereas heating occurs in the Abelian case. Estimates are provided for the cooling power produced by the non-Abelian anyon refrigerator, and its implementation in non-Abelian fractional quantum Hall liquids is discussed.We show in this Letter that the ground state degeneracy associated with the presence of non-Abelian anyons can be probed by using an adiabatic cooling process based on the non-Abelian entropy. In particular, we show that when the number of such anyons is increased adiabatically at sufficiently low temperatures, the non-Abelian liquid undergoes cooling, whereas heating occurs in the Abelian case. Estimates are provided for the cooling power produced by the non-Abelian anyon refrigerator, and its implementation in non-Abelian fractional quantum Hall liquids is discussed.

arXiv:1004.1580Physical Review LettersAug 16, 201015 citations

Topological Spin Derivation of Generalized Exclusion Statistics and Fano Factor in Fractional Quantum Hall States

Rowan Brad Quni-Gudzinas

The generalized exclusion statistics (GES) parameter $g$ characterizes the fractionalization of anyonic excitations in fractional quantum Hall (FQH) states. While $g$ is phenomenologically linked to the filling factor $\nu$ in Laughlin states, a universal derivation from the underlying topological field theory for arbitrary Abelian and non-Abelian states remains an open theoretical target. Furthermore, whether this topologically derived $g$ can quantitatively predict the shot-noise Fano factor $F$ measured in quantum point contact (QPC) tunneling experiments has not been rigorously established across general FQH phases. Here, we derive $g$ directly from the topological spin $\theta = e^{2\pi i h}$ , where $h$ is the conformal dimension of the corresponding conformal field theory (CFT) primary field. For Abelian anyons, $g = 2h$ , while non-Abelian anyons yield a matrix form. Using the Keldysh formalism for the QPC tunneling Hamiltonian, we show this topologically derived $g$ dictates the tunneling density of states exponent and predicts the Fano factor $F = g \nu$ in the weak backscattering regime. For Laughlin states at $\nu=1/m$ , this yields $F=\nu$ , matching fractional charge $e^*=\nu e$ . For non-Abelian states, the derived $g$ matrix predicts a modified Fano factor revealing topological spin contributions to nonequilibrium noise. ## 1. Introduction The fractional quantum Hall (FQH) effect provides a physical realization of topological phases of matter hosting anyonic excitations. These excitations obey generalized exclusion statistics (GES), a framework introduced to generalize the Pauli exclusion principle to particles with fractional braiding statistics. In a quantum point contact (QPC) geometry, the tunneling of these anyons generates shot noise, characterized by the Fano factor $F$ (the ratio of noise power to twice the Poissonian current). While the connection between GES and the filling factor $\nu$ is well-established for Laughlin states, a universal derivThe generalized exclusion statistics (GES) parameter $g$ characterizes the fractionalization of anyonic excitations in fractional quantum Hall (FQH) states. While $g$ is phenomenologically linked to the filling factor $\nu$ in Laughlin states, a universal derivation from the underlying topological field theory for arbitrary Abelian and non-Abelian states remains an open theoretical target. Furthermore, whether this topologically derived $g$ can quantitatively predict the shot-noise Fano factor $F$ measured in quantum point contact (QPC) tunneling experiments has not been rigorously established across general FQH phases. Here, we derive $g$ directly from the topological spin $\theta = e^{2\pi i h}$, where $h$ is the conformal dimension of the corresponding conformal field theory (CFT) primary field. For Abelian anyons, $g = 2h$, while non-Abelian anyons yield a matrix form. Using the Keldysh formalism for the QPC tunneling Hamiltonian, we show this topologically derived $g$ dictates the tunneling density of states exponent and predicts the Fano factor $F = g \nu$ in the weak backscattering regime. For Laughlin states at $\nu=1/m$, this yields $F=\nu$, matching fractional charge $e^*=\nu e$. For non-Abelian states, the derived $g$ matrix predicts a modified Fano factor revealing topological spin contributions to nonequilibrium noise. ## 1. Introduction The fractional quantum Hall (FQH) effect provides a physical realization of topological phases of matter hosting anyonic excitations. These excitations obey generalized exclusion statistics (GES), a framework introduced to generalize the Pauli exclusion principle to particles with fractional braiding statistics. In a quantum point contact (QPC) geometry, the tunneling of these anyons generates shot noise, characterized by the Fano factor $F$ (the ratio of noise power to twice the Poissonian current). While the connection between GES and the filling factor $\nu$ is well-established for Laughlin states, a universal deriv

Sep 4, 20260 citations

Fractional quantum Hall states as an Abelian group

Alí Nassar

arXiv:1403.7080Physics Letters ADec 22, 20140 citations

The generalized exclusion statistics (GES) parameter

g

characterizes the fractionalization of anyonic excitations in fractional quantum Hall (FQH) states. While

g

is phenomenologically linked to the filling factor

\nu

in Laughlin states, a universal derivation from the underlying topological field theory for arbitrary Abelian and non-Abelian states remains an open theoretical target. Furthermore, whether this topologically derived

g

can quantitatively predict the shot-noise Fano factor

F

measured in quantum point contact (QPC) tunneling experiments has not been rigorously established across general FQH phases. Here, we derive

g

directly from the topological spin

\theta = e^{2\pi i h}

, where

h

is the conformal dimension of the corresponding conformal field theory (CFT) primary field. For Abelian anyons,

g = 2h

, while non-Abelian anyons yield a matrix form. Using the Keldysh formalism for the QPC tunneling Hamiltonian, we show this topologically derived

g

dictates the tunneling density of states exponent and predicts the Fano factor

F = g \nu

in the weak backscattering regime. For Laughlin states at

\nu=1/m

, this yields

F=\nu

, matching fractional charge

e^*=\nu e

. For non-Abelian states, the derived

g

matrix predicts a modified Fano factor revealing topological spin contributions to nonequilibrium noise. ## 1. Introduction The fractional quantum Hall (FQH) effect provides a physical realization of topological phases of matter hosting anyonic excitations. These excitations obey generalized exclusion statistics (GES), a framework introduced to generalize the Pauli exclusion principle to particles with fractional braiding statistics. In a quantum point contact (QPC) geometry, the tunneling of these anyons generates shot noise, characterized by the Fano factor

F

(the ratio of noise power to twice the Poissonian current). While the connection between GES and the filling factor

\nu

is well-established for Laughlin states, a universal deriv