527 research outputs found
Kinematics nomenclature for physiological accelerations with special reference to vestibular applications
Kinematics nomenclature for physiological accelerations and special reference to vestibular apparatu
Elicitation of horizontal nystagmus by periodic linear acceleration
Horizontal nystagmus elicitation in man by periodic linear acceleratio
Recurrent proofs of the irrationality of certain trigonometric values
We use recurrences of integrals to give new and elementary proofs of the
irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all
nonzero rational r^2. Immediate consequences to other values of the elementary
transcendental functions are also discussed
On Local Equivalence, Surface Code States and Matroids
Recently, Ji et al disproved the LU-LC conjecture and showed that the local
unitary and local Clifford equivalence classes of the stabilizer states are not
always the same. Despite the fact this settles the LU-LC conjecture, a
sufficient condition for stabilizer states that violate the LU-LC conjecture is
missing. In this paper, we investigate further the properties of stabilizer
states with respect to local equivalence. Our first result shows that there
exist infinitely many stabilizer states which violate the LU-LC conjecture. In
particular, we show that for all numbers of qubits , there exist
distance two stabilizer states which are counterexamples to the LU-LC
conjecture. We prove that for all odd , there exist stabilizer
states with distance greater than two which are LU equivalent but not LC
equivalent. Two important classes of stabilizer states that are of great
interest in quantum computation are the cluster states and stabilizer states of
the surface codes. To date, the status of these states with respect to the
LU-LC conjecture was not studied. We show that, under some minimal
restrictions, both these classes of states preclude any counterexamples. In
this context, we also show that the associated surface codes do not have any
encoded non-Clifford transversal gates. We characterize the CSS surface code
states in terms of a class of minor closed binary matroids. In addition to
making connection with an important open problem in binary matroid theory, this
characterization does in some cases provide an efficient test for CSS states
that are not counterexamples.Comment: LaTeX, 13 pages; Revised introduction, minor changes and corrections
mainly in section V
Exactness of the Original Grover Search Algorithm
It is well-known that when searching one out of four, the original Grover's
search algorithm is exact; that is, it succeeds with certainty. It is natural
to ask the inverse question: If we are not searching one out of four, is
Grover's algorithm definitely not exact? In this article we give a complete
answer to this question through some rationality results of trigonometric
functions.Comment: 8 pages, 2 figure
Global periodicity conditions for maps and recurrences via Normal Forms
We face the problem of characterizing the periodic cases in parametric
families of (real or complex) rational diffeomorphisms having a fixed point.
Our approach relies on the Normal Form Theory, to obtain necessary conditions
for the existence of a formal linearization of the map, and on the introduction
of a suitable rational parametrization of the parameters of the family. Using
these tools we can find a finite set of values p for which the map can be
p-periodic, reducing the problem of finding the parameters for which the
periodic cases appear to simple computations. We apply our results to several
two and three dimensional classes of polynomial or rational maps. In particular
we find the global periodic cases for several Lyness type recurrences.Comment: 25 page
Otolith shear and the visual perception of force direction - Discrepancies and a proposed resolution
Otolith shear and visual perception of force direction with resolution of discrepancies by tangent equatio
Ground states for a class of deterministic spin models with glassy behaviour
We consider the deterministic model with glassy behaviour, recently
introduced by Marinari, Parisi and Ritort, with \ha\ , where is the discrete sine Fourier transform. The
ground state found by these authors for odd and prime is shown to
become asymptotically dege\-ne\-ra\-te when is a product of odd primes,
and to disappear for even. This last result is based on the explicit
construction of a set of eigenvectors for , obtained through its formal
identity with the imaginary part of the propagator of the quantized unit
symplectic matrix over the -torus.Comment: 15 pages, plain LaTe
An elementary algorithm to evaluate trigonometric functions to high precision
Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation
Perfect Transfer of Arbitrary States in Quantum Spin Networks
We propose a class of qubit networks that admit perfect state transfer of any
two-dimensional quantum state in a fixed period of time. We further show that
such networks can distribute arbitrary entangled states between two distant
parties, and can, by using such systems in parallel, transmit the higher
dimensional systems states across the network. Unlike many other schemes for
quantum computation and communication, these networks do not require qubit
couplings to be switched on and off. When restricted to -qubit spin networks
of identical qubit couplings, we show that is the maximal perfect
communication distance for hypercube geometries. Moreover, if one allows fixed
but different couplings between the qubits then perfect state transfer can be
achieved over arbitrarily long distances in a linear chain. This paper expands
and extends the work done in PRL 92, 187902.Comment: 12 pages, 3 figures with updated reference
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