scholarly journals Loop Quantum Gravity meets Topological Phases of Matter at the Black Hole horizon

2015 ◽  
Author(s):  
Andreas G. A. Pithis ◽  
Hans-Christian Ruiz Euler
Keyword(s):  
Quantum Gravity ◽  
Braid Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Two Dimensions ◽  
Simons Theory ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Flux Charge ◽  
Topological Quantum Computation

In this work we investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of Loop Quantum Gravity black holes by means of their relation to the braid group. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SU(2)_k-Chern-Simons theory explicitly exhibits non-abelian anyonic statistics, since the quantum gravitational degrees of freedom of the horizon can be seen as flux-charge composites. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1372-1378 ◽  
Author(s):  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
G. ZIKOS ◽  
S. H. SIMON
Keyword(s):  
Dimensional Space ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Operations ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
Two Space Dimensions ◽  
Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

scholarly journals ENTROPY AND AREA IN LOOP QUANTUM GRAVITY

2005 ◽  
Vol 14 (12) ◽  
pp. 2301-2305
Author(s):  
JOHN SWAIN
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Maximum Entropy ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Black Hole Entropy ◽  
Black Hole Thermodynamics ◽  
Three Dimensions ◽  
Spin Network

Black hole thermodynamics suggests that the maximum entropy that can be contained in a region of space is proportional to the area enclosing it rather than its volume. We argue that this follows naturally from loop quantum gravity and a result of Kolmogorov and Bardzin' on the the realizability of networks in three dimensions. This represents an alternative to other approaches in which some sort of correlation between field configurations helps limit the degrees of freedom within a region. It also provides an approach to thinking about black hole entropy in terms of states inside rather than on its surface. Intuitively, a spin network complicated enough to imbue a region with volume only lets that volume grow as quickly as the area bounding it.

Fermions, q-deformed diffeomorphism and the evolution of spin networks

2015 ◽  
Vol 24 (10) ◽  
pp. 1550074 ◽  
Author(s):  
L. Mullick ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Gravity ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Closed Loop ◽  
Direction Vector ◽  
Spin Networks ◽  
Spin Network ◽  
Diffeomorphism Invariance ◽  
Diffeomorphism Symmetry

We have considered here the emergence of diffeomorphism symmetry in quantum gravity in the framework of the quantization of a fermion. It is pointed out that a closed loop having the holonomy associated with the SU(2) gauge group is realized from the rotation of the direction vector associated with the quantization of a fermion depicting spin degrees of freedom which appear as SU(2) gauge bundle. During the formation of a loop, a noncyclic path with open ends can be mapped onto a closed loop when the holonomy involves q-deformed gauge group SUq(2). This gives rise to q-deformed diffeomorphism and helps to realize diffeomorphism invariance in quantum gravity through a sequence of q-deformed diffeomorphism in the limit q = 1. We can consider adiabatic iteration such that the quasispin associated with the quantum group SUq(2) gradually evolves as the time dependent deformation parameter q changes and in the limit q = 1, we achieve the standard spin. This essentially depicts the evolution of spin network as the loop is being formed and links fermionic degrees of freedom with loop quantum gravity.

scholarly journals Quantum Holography from Fermion Fields

2021 ◽  
Vol 3 (3) ◽  
pp. 576-591
Author(s):  
Paola Zizzi
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Boundary Surface ◽  
Holographic Principle ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Fermion Fields ◽  
Planck Unit

In this paper, we demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogolyubov transformations lead to pairs of the spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

scholarly journals ANYONIC TOPOLOGICAL QUANTUM COMPUTATION AND THE VIRTUAL BRAID GROUP

2011 ◽  
Vol 20 (01) ◽  
pp. 91-102
Author(s):  
H. A. DYE ◽  
LOUIS H. KAUFFMAN
Keyword(s):  
Quantum Computation ◽  
Braid Group ◽  
Topological Quantum ◽  
Topological Quantum Computation

We introduce a recoupling theory for virtual braided trees. This recoupling theory can be utilized to incorporate swap gates into anyonic models of quantum computation.

scholarly journals Quantum Holography from Fermion Fields

2021 ◽  
Author(s):  
Paola Zizzi
Keyword(s):  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Boundary Surface ◽  
Dimensional Sphere ◽  
Two Dimensional ◽  
Fuzzy Sphere ◽  
Fermion Fields ◽  
Planck Unit ◽  
Bogoliubov Transformations

We demonstrate, in the context of Loop Quantum Gravity, the Quantum Holographic Principle, according to which the area of the boundary surface enclosing a region of space encodes a qubit per Planck unit. To this aim, we introduce fermion fields in the bulk, whose boundary surface is the two-dimensional sphere. The doubling of the fermionic degrees of freedom and the use of the Bogoliubov transformations lead to pairs of spin network’s edges piercing the boundary surface with double punctures, giving rise to pixels of area encoding a qubit. The proof is also valid in the case of a fuzzy sphere.

scholarly journals Improved effective dynamics of loop-quantum-gravity black hole and Nariai limit

2021 ◽  
Author(s):  
Muxin Han ◽  
Hongguang Liu
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Degrees Of Freedom ◽  
Loop Quantum Gravity ◽  
Late Time ◽  
White Hole ◽  
Quantum Black Hole ◽  
Effective Dynamics ◽  
Symmetric Quantum ◽  
Space Formulation

Abstract We propose a new model of the spherical symmetric quantum black hole in the reduced phase space formulation. We deparametrize gravity by coupling to the Gaussian dust which provides the material coordinates. The foliation by dust coordinates covers both the interior and exterior of the black hole. After the spherical symmetry reduction, our model is a 1+1 dimensional field theory containing infinitely many degrees of freedom. The effective dynamics of the quantum black hole is generated by an improved physical Hamiltonian ${\bf H}_\Delta$. The holonomy correction in ${\bf H}_\Delta$ is implemented by the $\bar{\mu}$-scheme regularization with a Planckian area scale $\Delta$ (which often chosen as the minimal area gap in Loop Quantum Gravity). The effective dynamics recovers the semiclassical Schwarzschild geometry at low curvature regime and resolves the black hole singularity with Planckian curvature, e.g. $R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}\sim 1/{\Delta}^2$. Our model predicts that the evolution of the black hole at late time reaches the charged Nariai geometry ${\rm dS}_2\times S^2$ with Planckian radii $\sim \sqrt{\Delta}$. The Nariai geometry is stable under linear perturbations but may be unstable by nonperturbative quantum effects. Our model suggests the existence of quantum tunneling of the Nariai geometry and a scenario of black-hole-to-white-hole transition.

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