4,981 research outputs found
Quantum entanglement, unitary braid representation and Temperley-Lieb algebra
Important developments in fault-tolerant quantum computation using the
braiding of anyons have placed the theory of braid groups at the very
foundation of topological quantum computing. Furthermore, the realization by
Kauffman and Lomonaco that a specific braiding operator from the solution of
the Yang-Baxter equation, namely the Bell matrix, is universal implies that in
principle all quantum gates can be constructed from braiding operators together
with single qubit gates. In this paper we present a new class of braiding
operators from the Temperley-Lieb algebra that generalizes the Bell matrix to
multi-qubit systems, thus unifying the Hadamard and Bell matrices within the
same framework. Unlike previous braiding operators, these new operators
generate {\it directly}, from separable basis states, important entangled
states such as the generalized Greenberger-Horne-Zeilinger states, cluster-like
states, and other states with varying degrees of entanglement.Comment: 5 pages, no figur
Isoachlya, A New Genus Of The Saprolegniaceae
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141619/1/ajb205620.pd
The Genera Flammula And Paxillus And The Status Of The American Species
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141718/1/ajb205862.pd
Teleportation, Braid Group and Temperley--Lieb Algebra
We explore algebraic and topological structures underlying the quantum
teleportation phenomena by applying the braid group and Temperley--Lieb
algebra. We realize the braid teleportation configuration, teleportation
swapping and virtual braid representation in the standard description of the
teleportation. We devise diagrammatic rules for quantum circuits involving
maximally entangled states and apply them to three sorts of descriptions of the
teleportation: the transfer operator, quantum measurements and characteristic
equations, and further propose the Temperley--Lieb algebra under local unitary
transformations to be a mathematical structure underlying the teleportation. We
compare our diagrammatical approach with two known recipes to the quantum
information flow: the teleportation topology and strongly compact closed
category, in order to explain our diagrammatic rules to be a natural
diagrammatic language for the teleportation.Comment: 33 pages, 19 figures, latex. The present article is a short version
of the preprint, quant-ph/0601050, which includes details of calculation,
more topics such as topological diagrammatical operations and entanglement
swapping, and calls the Temperley--Lieb category for the collection of all
the Temperley--Lieb algebra with physical operations like local unitary
transformation
A Study Of The White Heart‐Rot Of Locust, Caused By Trametes Robiniophila
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141421/1/ajb205691.pd
Maximum Power Efficiency and Criticality in Random Boolean Networks
Random Boolean networks are models of disordered causal systems that can
occur in cells and the biosphere. These are open thermodynamic systems
exhibiting a flow of energy that is dissipated at a finite rate. Life does work
to acquire more energy, then uses the available energy it has gained to perform
more work. It is plausible that natural selection has optimized many biological
systems for power efficiency: useful power generated per unit fuel. In this
letter we begin to investigate these questions for random Boolean networks
using Landauer's erasure principle, which defines a minimum entropy cost for
bit erasure. We show that critical Boolean networks maximize available power
efficiency, which requires that the system have a finite displacement from
equilibrium. Our initial results may extend to more realistic models for cells
and ecosystems.Comment: 4 pages RevTeX, 1 figure in .eps format. Comments welcome, v2: minor
clarifications added, conclusions unchanged. v3: paper rewritten to clarify
it; conclusions unchange
Topological quantum gate entangler for a multi-qubit state
We establish a relation between topological and quantum entanglement for a
multi-qubit state by considering the unitary representations of the Artin braid
group. We construct topological operators that can entangle multi-qubit state.
In particular we construct operators that create quantum entanglement for
multi-qubit states based on the Segre ideal of complex multi-projective space.
We also in detail discuss and construct these operators for two-qubit and
three-qubit states.Comment: 6 page
Evolutionary dynamics on strongly correlated fitness landscapes
We study the evolutionary dynamics of a maladapted population of
self-replicating sequences on strongly correlated fitness landscapes. Each
sequence is assumed to be composed of blocks of equal length and its fitness is
given by a linear combination of four independent block fitnesses. A mutation
affects the fitness contribution of a single block leaving the other blocks
unchanged and hence inducing correlations between the parent and mutant
fitness. On such strongly correlated fitness landscapes, we calculate the
dynamical properties like the number of jumps in the most populated sequence
and the temporal distribution of the last jump which is shown to exhibit a
inverse square dependence as in evolution on uncorrelated fitness landscapes.
We also obtain exact results for the distribution of records and extremes for
correlated random variables
Quantum Invariants of Templates
We define invariants for templates that appear in certain dynamical systems. Invariants are derived from certain bialgebras. Diagrammatic relations between projections of templates and the algebraic structures are used to define invariants. We also construct 3-manifolds via framed links associated to tamplate diagrams, so that any 3-manifold invariant can be used as a template invariant
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