13,090 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 â 1} Ă ZN promised to be
injective for fixed b and satisfying f(b, x) = f(b + 1, x + s)
for b = 0, 1,...,M â 2, find the unknown shift s â 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 ïżœ, we give
an efficient (i.e., poly(logN)) quantum algorithm for this
problem provided M â„ N^â. The algorithm is based on the
âpretty good measurementâ and uses H. Lenstraâs (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
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
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
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
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
Generalized self-testing and the security of the 6-state protocol
Self-tested quantum information processing provides a means for doing useful
information processing with untrusted quantum apparatus. Previous work was
limited to performing computations and protocols in real Hilbert spaces, which
is not a serious obstacle if one is only interested in final measurement
statistics being correct (for example, getting the correct factors of a large
number after running Shor's factoring algorithm). This limitation was shown by
McKague et al. to be fundamental, since there is no way to experimentally
distinguish any quantum experiment from a special simulation using states and
operators with only real coefficients.
In this paper, we show that one can still do a meaningful self-test of
quantum apparatus with complex amplitudes. In particular, we define a family of
simulations of quantum experiments, based on complex conjugation, with two
interesting properties. First, we are able to define a self-test which may be
passed only by states and operators that are equivalent to simulations within
the family. This extends work of Mayers and Yao and Magniez et al. in
self-testing of quantum apparatus, and includes a complex measurement. Second,
any of the simulations in the family may be used to implement a secure 6-state
QKD protocol, which was previously not known to be implementable in a
self-tested framework.Comment: To appear in proceedings of TQC 201
Perspective review of what is needed for molecular-specific fluorescence-guided surgery
Molecular image-guided surgery has the potential for translating the tools of molecular pathology to real-time guidance in surgery. As a whole, there are incredibly positive indicators of growth, including the first United States Food and Drug Administration clearance of an enzyme-biosynthetic-activated probe for surgery guidance, and a growing number of companies producing agents and imaging systems. The strengths and opportunities must be continued but are hampered by important weaknesses and threats within the field. A key issue to solve is the inability of macroscopic imaging tools to resolve microscopic biological disease heterogeneity and the limitations in microscopic systems matching surgery workflow. A related issue is that parsing out true molecular-specific uptake from simple-enhanced permeability and retention is hard and requires extensive pathologic analysis or multiple in vivo tests, comparing fluorescence accumulation with standard histopathology and immunohistochemistry. A related concern in the field is the over-reliance on a finite number of chosen preclinical models, leading to early clinical translation when the probe might not be optimized for high intertumor variation or intratumor heterogeneity. The ultimate potential may require multiple probes, as are used in molecular pathology, and a combination with ultrahigh-resolution imaging and image recognition systems, which capture the data at a finer granularity than is possible by the surgeon. Alternatively, one might choose a more generalized approach by developing the tracer based on generic hallmarks of cancer to create a more "one-size-fits-all" concept, similar to metabolic aberrations as exploited in fluorodeoxyglucose-positron emission tomography (FDG-PET) (i.e., Warburg effect) or tumor acidity. Finally, methods to approach the problem of production cost minimization and regulatory approvals in a manner consistent with the potential revenue of the field will be important. In this area, some solid steps have been demonstrated in the use of fluorescent labeling commercial antibodies and separately in microdosing studies with small molecules. (C) The Authors
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