51 research outputs found
Topological quantum buses: coherent quantum information transfer between topological and conventional qubits
We propose computing bus devices that enable quantum information to be
coherently transferred between topological and conventional qubits. We describe
a concrete realization of such a topological quantum bus acting between a
topological qubit in a Majorana wire network and a conventional semiconductor
double quantum dot qubit. Specifically, this device measures the joint
(fermion) parity of these two different qubits by using the Aharonov-Casher
effect in conjunction with an ancilliary superconducting flux qubit that
facilitates the measurement. Such a parity measurement, together with the
ability to apply Hadamard gates to the two qubits, allows one to produce states
in which the topological and conventional qubits are maximally entangled and to
teleport quantum states between the topological and conventional quantum
systems.Comment: 5 pages, 2 figures; v2: minor revision
Interface Between Topological and Superconducting Qubits
We propose and analyze an interface between a topological qubit and a
superconducting flux qubit. In our scheme, the interaction between Majorana
fermions in a topological insulator is coherently controlled by a
superconducting phase that depends on the quantum state of the flux qubit. A
controlled phase gate, achieved by pulsing this interaction on and off, can
transfer quantum information between the topological qubit and the
superconducting qubit.Comment: 12 pages, 7 figures. V2: Final version as published in Phys. Rev.
Lett, with detailed clarifications in the Appendi
Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states
Utilizing large-scale Monte-Carlo simulations, we investigate an
unconventional two-component classical plasma in two dimensions which controls
the behavior of the norms and overlaps of the quantum-mechanical wavefunctions
of Ising-type quantum Hall states. The plasma differs fundamentally from that
which is associated with the two-dimensional XY model and Abelian fractional
quantum Hall states. We find that this unconventional plasma undergoes a
Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal.
The parameter values corresponding to Ising-type quantum Hall states lie on the
metallic side of this transition. This result verifies the required properties
of the unconventional plasma used to demonstrate that Ising-type quantum Hall
states possess quasiparticles with non-Abelian braiding statistics.Comment: 16 pages, 14 figures. Submitted to Physical Review
Clebsch-Gordan and 6j-coefficients for rank two quantum groups
We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two
quantum groups. We explain in detail how such calculations are done, which
should allow the reader to perform similar calculations in other cases.
Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as
well as some other topological data associated with theories corresponding to
rank-two quantum groups. Finally, we collect some useful properties of the
fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica
notebooks containing the various q-CG and 6j symbols, see
http://arxiv.org/src/1004.5456/an
Non-Abelian statistics and topological quantum information processing in 1D wire networks
Topological quantum computation provides an elegant way around decoherence,
as one encodes quantum information in a non-local fashion that the environment
finds difficult to corrupt. Here we establish that one of the key
operations---braiding of non-Abelian anyons---can be implemented in
one-dimensional semiconductor wire networks. Previous work [Lutchyn et al.,
arXiv:1002.4033 and Oreg et al., arXiv:1003.1145] provided a recipe for driving
semiconducting wires into a topological phase supporting long-sought particles
known as Majorana fermions that can store topologically protected quantum
information. Majorana fermions in this setting can be transported, created, and
fused by applying locally tunable gates to the wire. More importantly, we show
that networks of such wires allow braiding of Majorana fermions and that they
exhibit non-Abelian statistics like vortices in a p+ip superconductor. We
propose experimental setups that enable the Majorana fusion rules to be probed,
along with networks that allow for efficient exchange of arbitrary numbers of
Majorana fermions. This work paves a new path forward in topological quantum
computation that benefits from physical transparency and experimental realism.Comment: 6 pages + 17 pages of Supp. Mat.; 10 figures. Supp. Mat. has doubled
in size to establish results more rigorously; many other improvements as wel
Non-locality of non-Abelian anyons
Topological systems, such as fractional quantum Hall liquids, promise to
successfully combat environmental decoherence while performing quantum
computation. These highly correlated systems can support non-Abelian anyonic
quasiparticles that can encode exotic entangled states. To reveal the non-local
character of these encoded states we demonstrate the violation of suitable Bell
inequalities. We provide an explicit recipe for the preparation, manipulation
and measurement of the desired correlations for a large class of topological
models. This proposal gives an operational measure of non-locality for anyonic
states and it opens up the possibility to violate the Bell inequalities in
quantum Hall liquids or spin lattices.Comment: 7 pages, 3 figure
The non-Abelian Interferometer
We consider the tunneling current through a double point-contact Fabry-Perot
interferometer such as used in recent experimental studies of the fractional
quantum Hall plateau at filling fraction nu=5/2. We compare the predictions of
several different models of the state of the electrons at this plateau: the
Moore-Read, anti-Pfaffian, SU(2)_2 NAF, K=8 strong pairing, and (3,3,1) states.
All of these predict the existence of charge e/4 quasiparticles, but the first
three are non-Abelian while the last two are Abelian. We give explicit formulas
for the scaling of charge e/2 and charge e/4 quasiparticle contributions to the
current as a function of temperature, gate voltage and distance between the two
point contacts for all three models. Based on these, we analyze several
possible explanations of two phenomena reported for recent experiments by
Willett et al., namely halving of the period of the observed resistance
oscillations with rising temperature and alternation between the same two
observed periods at low temperatures as the area of the interference loop is
varied with a side gate. We conclude that the most likely explanation is that
the observed alternation is due to switching between even and odd numbers of
charge e/4 quasiparticles enclosed within the loop as a function of side gate
voltage, which is a clear signature of the presence of non-Abelian anyons.
However, there are important features of the data which do not have a simple
explanation within this picture. We suggest further experiments which could
help rule out some possible scenarios. We make the corresponding predictions
for future tunneling and interference experiments at the other observed second
Landau level fractional quantum Hall states.Comment: 15 pages, 1 figure; v2: additional discussions and references added;
v3: clarifications and references updated; Appendix C has been removed and
incorporated in arXiv:0909.1056; this paper has been given the more clear,
accurate, and informative title "Interferometric signature of non-Abelian
anyons" in PRB by its editor
Anyons in a weakly interacting system
We describe a theoretical proposal for a system whose excitations are anyons
with the exchange phase pi/4 and charge -e/2, but, remarkably, can be built by
filling a set of single-particle states of essentially noninteracting
electrons. The system consists of an artificially structured type-II
superconducting film adjacent to a 2D electron gas in the integer quantum Hall
regime with unit filling fraction. The proposal rests on the observation that a
vacancy in an otherwise periodic vortex lattice in the superconductor creates a
bound state in the 2DEG with total charge -e/2. A composite of this
fractionally charged hole and the missing flux due to the vacancy behaves as an
anyon. The proposed setup allows for manipulation of these anyons and could
prove useful in various schemes for fault-tolerant topological quantum
computation.Comment: 7 pages with 3 figures. For related work and info visit
http://www.physics.ubc.ca/~fran
Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2
Recent theories suggest that the excitations of certain quantum Hall states
may have exotic braiding statistics which could be used to build topological
quantum gates. This has prompted an experimental push to study such states
using confined geometries where the statistics can be tested. We study the
transport properties of quantum point contacts (QPCs) fabricated on a
GaAs/AlGaAs two dimensional electron gas that exhibits well-developed
fractional quantum Hall effect, including at bulk filling fraction 5/2. We find
that a plateau at effective QPC filling factor 5/2 is identifiable in point
contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5
microns. We study the temperature and dc-current-bias dependence of the 5/2
plateau in the QPC, as well as neighboring fractional and integer plateaus in
the QPC while keeping the bulk at filling factor 3. Transport near QPC filling
factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states
with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms
in this confined geometry
Towards identification of a non-abelian state: observation of a quarter of electron charge at quantum Hall state
The fractional quantum Hall effect, where plateaus in the Hall resistance at
values of coexist with zeros in the longitudinal resistance, results from
electron correlations in two dimensions under a strong magnetic field. Current
flows along the edges carried by charged excitations (quasi particles) whose
charge is a fraction of the electron charge. While earlier research
concentrated on odd denominator fractional values of , the observation of
the even denominator state sparked a vast interest. This state is
conjectured to be characterized by quasiparticles of charge e/4, whose
statistics is non-abelian. In other words, interchanging of two quasi particles
may modify the state of the system to an orthogonal one, and does not just add
a phase as in for fermions or bosons. As such, these quasiparticles may be
useful for the construction of a topological quantum computer. Here we report
data of shot noise generated by partitioning edge currents in the
state, consistent with the charge of the quasiparticle being e/4, and
inconsistent with other potentially possible values, such as e/2 and e. While
not proving the non-abelian nature of the state, this observation is
the first step toward a full understanding of these new fractional charges
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