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 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.

scholarly journals Exact Modular $S$ Matrix for ${\mathbb Z}_{k}$ Parafermion Quantum Hall Islands and Measurement of Non-Abelian Anyons

2021 ◽  
Vol 62 ◽  
pp. 1-28
Author(s):  
Lachezar S. Georgiev ◽  
Keyword(s):  
Quantum Hall ◽  
Affine Lie Algebras ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Topological Quantum ◽  
S Matrix ◽  
Topological Quantum Computation ◽  
Charged Sector ◽  
Coset Models

Using the decomposition of rational conformal filed theory characters for the $\Z_k$ parafermion quantum Hall droplets for general $k=2,3,\dots$, we derive analytically the full modular $S$ matrix for these states, including the $\uu$ parts corresponding to the charged sector of the full conformal field theory and the neutral parafermion contributions corresponding to the diagonal affine coset models. This precise neutral-part parafermion $S$ matrix is derived from the explicit relations between the coset matrix and those for the numerator and denominator of the coset and the latter is expressed in compact form due to the level-rank duality between the affine Lie algebras $\widehat{\frak{su}(k)_2}$ and $\widehat{\frak{su}(2)_k}$. The exact results obtained for the $S$ matrix elements are expected to play an important role for identifying interference patterns of fractional quantum Hall states in Fabry-P\'erot interferometers which can be used to distinguish between Abelian and non-Abelian statistics of quasiparticles localized in the bulk of fractional quantum Hall droplets as well as for nondestructive interference measurement of Fibonacci anyons which can be used for universal topological quantum computation

Fractionally charged BPS particles in M-string on 3D orbifolds

2021 ◽  
Author(s):  
S. Boukaddid ◽  
R. Ahl Laamara ◽  
L. B. Drissi ◽  
E. H. Saidi ◽  
J. Zerouaoui
Keyword(s):  
Quantum Hall ◽  
Three Dimensional ◽  
Particle Spectrum ◽  
Gauge Bosons ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Conformal Field ◽  
Super Conformal Field Theory ◽  
Bps States ◽  
Chern Simons

In this paper, we study the M-string realization of chiral [Formula: see text]-super-conformal field theory in 6 dimensions and its orbifold compactification down to three-dimensional (3D). We analyze its fractionally charged BPS particle spectrum in connection with effective 3D Chern–Simons gauge theory and the supersymmetric fractional quantum Hall effect in [Formula: see text] dimensions. We construct the set of underlying fractionally charged BPS particles in the ground state of the compactified M string and find that it contains 144 BPS states that are generated by four basic quasi-particles (two bosonic-like and two fermionic like) and their CPT conjugate. Two representations of the gauge bosons and the gauginos as condensates of the basic quasiparticles are found and explicit realizations are also given. Other features concerning generalizations are also discussed.

scholarly journals From Chern–Simons to Tomonaga–Luttinger

2018 ◽  
Vol 33 (02) ◽  
pp. 1850013 ◽  
Author(s):  
Nicola Maggiore
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Weyl Fermion

A single-sided boundary is introduced in the three-dimensional Chern–Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for the two-dimensional Weyl fermion describing the degrees of freedom of the edge states of the Fractional Quantum Hall Effect. The symmetry on the boundary is derived, which determines the effective two-dimensional action, whose equation of motion coincides with the continuity equation of the Tomonaga–Luttinger theory. The role of Lorentz symmetry and of discrete symmetries on the boundary is also discussed.

BRAIDING AND ENTANGLEMENT IN NONABELIAN QUANTUM HALL STATES

2009 ◽  
Vol 23 (12n13) ◽  
pp. 2727-2736 ◽  
Author(s):  
G. ZIKOS ◽  
K. YANG ◽  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
S. H. SIMON
Keyword(s):  
Quantum Computation ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Dimensional Space ◽  
Quantum Hall ◽  
Topological Order ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Topological Quantum ◽  
Hall States

Certain fractional quantum Hall states, including the experimentally observed ν = 5/2 state, and, possibly, the ν = 12/5 state, may have a sufficiently rich form of topological order (i.e. they may be nonabelian) to be useful for quantum information processing. For example, in some cases they may be used for topological quantum computation, an intrinsically fault tolerant form of quantum computation which is carried out by braiding the world lines of quasiparticle excitations in 2+1 dimensional space time. Here we briefly review the relevant properties of nonabelian quantum Hall states and discuss some of the methods we have found for finding specific braiding patterns which can be used to carry out universal quantum computation using them. Recent work on one-dimensional chains of interacting quasiparticles in nonabelian states is also reviewed.

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