1,803 research outputs found
Topological Quantum Computation
The theory of quantum computation can be constructed from the abstract study
of anyonic systems. In mathematical terms, these are unitary topological
modular functors. They underlie the Jones polynomial and arise in
Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in
quantum Hall electron liquids and 2D-magnets are modeled by modular functors,
opening a new possibility for the realization of quantum computers. The chief
advantage of anyonic computation would be physical error correction: An error
rate scaling like e^{-\a\l}, where \l is a length scale, and is
some positive constant. In contrast, the \qpresumptive" qubit-model of
quantum computation, which repairs errors combinatorically, requires a
fantastically low initial error rate (about ) before computation can
be stabilized
Measurement-Only Topological Quantum Computation
We remove the need to physically transport computational anyons around each
other from the implementation of computational gates in topological quantum
computing. By using an anyonic analog of quantum state teleportation, we show
how the braiding transformations used to generate computational gates may be
produced through a series of topological charge measurements.Comment: 5 pages, 2 figures; v2: clarifying changes made to conform to the
version published in PR
Towards Universal Topological Quantum Computation in the Fractional Quantum Hall State
The Pfaffian state, which may describe the quantized Hall plateau observed at
Landau level filling fraction , can support topologically-protected
qubits with extremely low error rates. Braiding operations also allow perfect
implementation of certain unitary transformations of these qubits. However, in
the case of the Pfaffian state, this set of unitary operations is not quite
sufficient for universal quantum computation (i.e. is not dense in the unitary
group). If some topologically unprotected operations are also used, then the
Pfaffian state supports universal quantum computation, albeit with some
operations which require error correction. On the other hand, if certain
topology-changing operations can be implemented, then fully
topologically-protected universal quantum computation is possible. In order to
accomplish this, it is necessary to measure the interference between
quasiparticle trajectories which encircle other moving trajectories in a
time-dependent Hall droplet geometry.Comment: A related paper, cond-mat/0512072, explains the topological issues in
greater detail. It may help the reader to look at this alternate presentation
if confused about any poin
Holographic RG-flows and Boundary CFTs
Solutions of -dimensional gravity coupled to a scalar field are
obtained, which holographically realize interface and boundary CFTs. The
solution utilizes a Janus-like slicing ansatz and corresponds
to a deformation of the CFT by a spatially-dependent coupling of a relevant
operator. The BCFT solutions are singular in the bulk, but physical quantities
such as the holographic entanglement entropy can be calculated.Comment: 26 pages, 11 figure
Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
The Pfaffian state is an attractive candidate for the observed quantized Hall
plateau at Landau level filling fraction . This is particularly
intriguing because this state has unusual topological properties, including
quasiparticle excitations with non-Abelian braiding statistics. In order to
determine the nature of the state, one must measure the quasiparticle
braiding statistics. Here, we propose an experiment which can simultaneously
determine the braiding statistics of quasiparticle excitations and, if they
prove to be non-Abelian, produce a topologically-protected qubit on which a
logical NOT operation is performed by quasiparticle braiding. Using the
measured excitation gap at , we estimate the error rate to be
or lower
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