17,254 research outputs found
Quantum algorithm for a generalized hidden shift problem
Consider the following generalized hidden shift problem:
given a function f on {0,...,M − 1} × ZN promised to be
injective for fixed b and satisfying f(b, x) = f(b + 1, x + s)
for b = 0, 1,...,M − 2, find the unknown shift s ∈ ZN.
For M = N, this problem is an instance of the abelian
hidden subgroup problem, which can be solved efficiently on
a quantum computer, whereas for M = 2, it is equivalent
to the dihedral hidden subgroup problem, for which no
efficient algorithm is known. For any fixed positive �, we give
an efficient (i.e., poly(logN)) quantum algorithm for this
problem provided M ≥ N^∈. The algorithm is based on the
“pretty good measurement” and uses H. Lenstra’s (classical)
algorithm for integer programming as a subroutine
Some Implications on Amorphic Association Schemes
AMS classifications: 05E30, 05B20;amorphic association scheme;strongly regular graph;(negative) Latin square type;cyclotomic association scheme;strongly regular decomposition
The Euler current and relativistic parity odd transport
For a spacetime of odd dimensions endowed with a unit vector field, we
introduce a new topological current that is identically conserved and whose
charge is equal to the Euler character of the even dimensional spacelike
foliations. The existence of this current allows us to introduce new
Chern-Simons-type terms in the effective field theories describing relativistic
quantum Hall states and (2+1) dimensional superfluids. Using effective field
theory, we calculate various correlation functions and identify transport
coefficients. In the quantum Hall case, this current provides the natural
relativistic generalization of the Wen-Zee term, required to characterize the
shift and Hall viscosity in quantum Hall systems. For the superfluid case this
term is required to have nonzero Hall viscosity and to describe superfluids
with non s-wave pairing.Comment: 24 pages. v2: added citations, corrected minor typos in appendi
From optimal measurement to efficient quantum algorithms for the hidden subgroup problem over semidirect product groups
We approach the hidden subgroup problem by performing the so-called pretty
good measurement on hidden subgroup states. For various groups that can be
expressed as the semidirect product of an abelian group and a cyclic group, we
show that the pretty good measurement is optimal and that its probability of
success and unitary implementation are closely related to an average-case
algebraic problem. By solving this problem, we find efficient quantum
algorithms for a number of nonabelian hidden subgroup problems, including some
for which no efficient algorithm was previously known: certain metacyclic
groups as well as all groups of the form (Z_p)^r X| Z_p for fixed r (including
the Heisenberg group, r=2). In particular, our results show that entangled
measurements across multiple copies of hidden subgroup states can be useful for
efficiently solving the nonabelian HSP.Comment: 18 pages; v2: updated references on optimal measuremen
Effective Field Theory of Relativistic Quantum Hall Systems
Motivated by the observation of the fractional quantum Hall effect in
graphene, we consider the effective field theory of relativistic quantum Hall
states. We find that, beside the Chern-Simons term, the effective action also
contains a term of topological nature, which couples the electromagnetic field
with a topologically conserved current of dimensional relativistic fluid.
In contrast to the Chern-Simons term, the new term involves the spacetime
metric in a nontrivial way. We extract the predictions of the effective theory
for linear electromagnetic and gravitational responses. For fractional quantum
Hall states at the zeroth Landau level, additional holomorphic constraints
allow one to express the results in terms of two dimensionless constants of
topological nature.Comment: 4 page
Some Spectral and Quasi-Spectral Characterizations of Distance-Regular Graphs
In this paper we consider the concept of preintersection numbers of a graph.
These numbers are determined by the spectrum of the adjacency matrix of the
graph, and generalize the intersection numbers of a distance-regular graph. By
using the preintersection numbers we give some new spectral and quasi-spectral
characterizations of distance-regularity, in particular for graphs with large
girth or large odd-girth
Uniformity in Association schemes and Coherent Configurations: Cometric Q-Antipodal Schemes and Linked Systems
2010 Mathematics Subject Classification. Primary 05E30, Secondary 05B25, 05C50, 51E12
Improving water productivity in agriculture in developing economies: in search of new avenues
Water ProductivityCrop productionWheatCottonEvapotranspirationEcnomic aspects
Modeling low order aberrations in laser guide star adaptive optics systems
When using a laser guide star (LGS) adaptive optics (AO) system, quasi-static aberrations are observed between the measured wavefronts from the LGS wavefront sensor (WFS) and the natural guide star (NGS) WFS. These LGS aberrations, which can be as much as 1200 nm RMS on the Keck II LGS AO system, arise due to the finite height and structure of the sodium layer. The LGS aberrations vary significantly between nights due to the difference in sodium structure. In this paper, we successfully model these LGS aberrations for the Keck II LGS AO system. We use this model to characterize the LGS aberrations as a function of pupil angle, elevation, sodium structure, uplink tip/tilt error, detector field of view, the number of detector pixels, and seeing. We also employ the model to estimate the LGS aberrations for the Palomar LGS AO system, the planned Keck I and the Thirty Meter Telescope (TMT) LGS AO systems. The LGS aberrations increase with increasing telescope diameter, but are reduced by central projection of the laser compared to side projection
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