16,302 research outputs found
Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation
Universal quantum computation on decoherence-free subspaces and subsystems
(DFSs) is examined with particular emphasis on using only physically relevant
interactions. A necessary and sufficient condition for the existence of
decoherence-free (noiseless) subsystems in the Markovian regime is derived here
for the first time. A stabilizer formalism for DFSs is then developed which
allows for the explicit understanding of these in their dual role as quantum
error correcting codes. Conditions for the existence of Hamiltonians whose
induced evolution always preserves a DFS are derived within this stabilizer
formalism. Two possible collective decoherence mechanisms arising from
permutation symmetries of the system-bath coupling are examined within this
framework. It is shown that in both cases universal quantum computation which
always preserves the DFS (*natural fault-tolerant computation*) can be
performed using only two-body interactions. This is in marked contrast to
standard error correcting codes, where all known constructions using one or
two-body interactions must leave the codespace during the on-time of the
fault-tolerant gates. A further consequence of our universality construction is
that a single exchange Hamiltonian can be used to perform universal quantum
computation on an encoded space whose asymptotic coding efficiency is unity.
The exchange Hamiltonian, which is naturally present in many quantum systems,
is thus *asymptotically universal*.Comment: 40 pages (body: 30, appendices: 3, figures: 5, references: 2). Fixed
problem with non-printing figures. New references added, minor typos
correcte
Robust Processing of Natural Language
Previous approaches to robustness in natural language processing usually
treat deviant input by relaxing grammatical constraints whenever a successful
analysis cannot be provided by ``normal'' means. This schema implies, that
error detection always comes prior to error handling, a behaviour which hardly
can compete with its human model, where many erroneous situations are treated
without even noticing them.
The paper analyses the necessary preconditions for achieving a higher degree
of robustness in natural language processing and suggests a quite different
approach based on a procedure for structural disambiguation. It not only offers
the possibility to cope with robustness issues in a more natural way but
eventually might be suited to accommodate quite different aspects of robust
behaviour within a single framework.Comment: 16 pages, LaTeX, uses pstricks.sty, pstricks.tex, pstricks.pro,
pst-node.sty, pst-node.tex, pst-node.pro. To appear in: Proc. KI-95, 19th
German Conference on Artificial Intelligence, Bielefeld (Germany), Lecture
Notes in Computer Science, Springer 199
Empirical Determination of Bang-Bang Operations
Strong and fast "bang-bang" (BB) pulses have been recently proposed as a
means for reducing decoherence in a quantum system. So far theoretical analysis
of the BB technique relied on model Hamiltonians. Here we introduce a method
for empirically determining the set of required BB pulses, that relies on
quantum process tomography. In this manner an experimenter may tailor his or
her BB pulses to the quantum system at hand, without having to assume a model
Hamiltonian.Comment: 14 pages, 2 eps figures, ReVTeX4 two-colum
Probabilistic Motion Estimation Based on Temporal Coherence
We develop a theory for the temporal integration of visual motion motivated
by psychophysical experiments. The theory proposes that input data are
temporally grouped and used to predict and estimate the motion flows in the
image sequence. This temporal grouping can be considered a generalization of
the data association techniques used by engineers to study motion sequences.
Our temporal-grouping theory is expressed in terms of the Bayesian
generalization of standard Kalman filtering. To implement the theory we derive
a parallel network which shares some properties of cortical networks. Computer
simulations of this network demonstrate that our theory qualitatively accounts
for psychophysical experiments on motion occlusion and motion outliers.Comment: 40 pages, 7 figure
Protected gates for topological quantum field theories
We study restrictions on locality-preserving unitary logical gates for
topological quantum codes in two spatial dimensions. A locality-preserving
operation is one which maps local operators to local operators --- for example,
a constant-depth quantum circuit of geometrically local gates, or evolution for
a constant time governed by a geometrically-local bounded-strength Hamiltonian.
Locality-preserving logical gates of topological codes are intrinsically fault
tolerant because spatially localized errors remain localized, and hence
sufficiently dilute errors remain correctable. By invoking general properties
of two-dimensional topological field theories, we find that the
locality-preserving logical gates are severely limited for codes which admit
non-abelian anyons; in particular, there are no locality-preserving logical
gates on the torus or the sphere with M punctures if the braiding of anyons is
computationally universal. Furthermore, for Ising anyons on the M-punctured
sphere, locality-preserving gates must be elements of the logical Pauli group.
We derive these results by relating logical gates of a topological code to
automorphisms of the Verlinde algebra of the corresponding anyon model, and by
requiring the logical gates to be compatible with basis changes in the logical
Hilbert space arising from local F-moves and the mapping class group.Comment: 50 pages, many figures, v3: updated to match published versio
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