1,382 research outputs found
Topological Quantum Computing
This set of lecture notes forms the basis of a series of lectures delivered
at the 48th IFF Spring School 2017 on Topological Matter: Topological
Insulators, Skyrmions and Majoranas at Forschungszentrum Juelich, Germany. The
first part of the lecture notes covers the basics of abelian and non-abelian
anyons and their realization in the Kitaev's honeycomb model. The second part
discusses how to perform universal quantum computation using Majorana fermions.Comment: In Topological Matter: Topological Insulators, Skyrmions and
Majoranas, Lecture notes of the 48th IFF Spring School 2017, eds. S. Bluegel,
Y. Mokrusov, T. Schaepers, and Y. Ando (Forschungszentrum Juelich, Key
Technologies, Vol. 139, 2017), Sec. D
Topological Quantum Computing and the Jones Polynomial
In this paper, we give a description of a recent quantum algorithm created by
Aharonov, Jones, and Landau for approximating the values of the Jones
polynomial at roots of unity of the form exp(2i/k). This description is
given with two objectives in mind. The first is to describe the algorithm in
such a way as to make explicit the underlying and inherent control structure.
The second is to make this algorithm accessible to a larger audience.Comment: 19 pages, 27 figure
Topological Quantum Computing with p-Wave Superfluid Vortices
It is shown that Majorana fermions trapped in three vortices in a p-wave
superfluid form a qubit in a topological quantum computing (TQC). Several
similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. {\bf 86},
268 (2001)] and Zhang {\it et al.} [Phys. Rev. Lett. {\bf 99}, 220502 (2007)]
have proposed schemes in which a qubit is implemented with two and four
Majorana fermions, respectively, where a qubit operation is performed by
exchanging the positions of Majorana fermions. The set of gates thus obtained
is a discrete subset of the relevant unitary group. We propose, in this paper,
a new scheme, where three Majorana fermions form a qubit. We show that
continuous 1-qubit gate operations are possible by exchanging the positions of
Majorana fermions complemented with dynamical phase change. 2-qubit gates are
realized through the use of the coupling between Majorana fermions of different
qubits.Comment: 5 pages, 2 figures. Two-qubit gate implementation is added
Topological Quantum Computing with Only One Mobile Quasiparticle
In a topological quantum computer, universal quantum computation is performed
by dragging quasiparticle excitations of certain two dimensional systems around
each other to form braids of their world lines in 2+1 dimensional space-time.
In this paper we show that any such quantum computation that can be done by
braiding identical quasiparticles can also be done by moving a single
quasiparticle around n-1 other identical quasiparticles whose positions remain
fixed.Comment: 4 pages, 5 figure
Constructing Functional Braids for Low-Leakage Topological Quantum Computing
We discuss how to significantly reduce leakage errors in topological quantum
computation by introducing an irrelevant error in phase, using the construction
of a CNOT gate in the Fibonacci anyon model as a concrete example. To be
specific, we construct a functional braid in a six-anyon Hilbert space that
exchanges two neighboring anyons while conserving the encoded quantum
information. The leakage error is for a braid of 100
interchanges of anyons. Applying the braid greatly reduces the leakage error in
the construction of generic controlled-rotation gates.Comment: 5 pages, 4 figures, updated, accepeted by Phys. Rev.
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