162 research outputs found
Measurement-Only Topological Quantum Computation via Anyonic Interferometry
We describe measurement-only topological quantum computation using both
projective and interferometrical measurement of topological charge. We
demonstrate how anyonic teleportation can be achieved using "forced
measurement" protocols for both types of measurement. Using this, it is shown
how topological charge measurements can be used to generate the braiding
transformations used in topological quantum computation, and hence that the
physical transportation of computational anyons is unnecessary. We give a
detailed discussion of the anyonics for implementation of topological quantum
computation (particularly, using the measurement-only approach) in fractional
quantum Hall systems.Comment: 57 pages, 5 figures; v2: minor correction
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
Probing Non-Abelian Statistics with QuasiParticle Interferometry
We examine interferometric experiments in systems that exhibit non-Abelian
braiding statistics, expressing outcomes in terms of the modular S-matrix. In
particular, this result applies to FQH interferometry, and we give a detailed
treatment of the Read-Rezayi states, providing explicit predictions for the
recently observed nu=12/5 plateau.Comment: 5 pages, 1 figure; v2: references added, orientation convention of
the modular S-matrix changed, clarification regarding particle-hole
transformation added; v3: references updated, clarifying changes made to
conform to the version published in PR
Search for electron liquids with non-Abelian quasiparticles
We use exact numerical diagonalization in the search of fractional quantum
Hall states with non-Abelian quasiparticle statistics. For the (most promising)
states in a partially filled second Landau level, the search is narrowed to the
range of filling factors . In this range, the analysis of
energy spectra and correlation functions, calculated including finite width and
Landau level mixing, supports the prominent non-Abelian candidates at
(paired Moore--Read "pfafian" state) and 12/5 (clustered
Read--Rezayi "parafermion" state). Outside of this range, the noninteracting
composite fermion model with four attached flux quanta is validated, yielding
the family of quantum liquids with fractional, but Abelian statistics. The
borderline state is shown to be adiabatically connected to the
Laughlin liquid, but its short-range correlations are significantly different.Comment: 9 pages, 8 figure
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