5,436 research outputs found
Introduction to Quantum Information Processing
As a result of the capabilities of quantum information, the science of
quantum information processing is now a prospering, interdisciplinary field
focused on better understanding the possibilities and limitations of the
underlying theory, on developing new applications of quantum information and on
physically realizing controllable quantum devices. The purpose of this primer
is to provide an elementary introduction to quantum information processing, and
then to briefly explain how we hope to exploit the advantages of quantum
information. These two sections can be read independently. For reference, we
have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at
http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at
http://www.c3.lanl.gov/~knill/qip/prhtm
Cohomology for Anyone
Crystallography has proven a rich source of ideas over several centuries.
Among the many ways of looking at space groups, N. David Mermin has pioneered
the Fourier-space approach. Recently, we have supplemented this approach with
methods borrowed from algebraic topology. We now show what topology, which
studies global properties of manifolds, has to do with crystallography. No
mathematics is assumed beyond what the typical physics or crystallography
student will have seen of group theory; in particular, the reader need not have
any prior exposure to topology or to cohomology of groups.Comment: 21 pages + figures, bibliography, Mathematica code homology.
Quantum algorithms for problems in number theory, algebraic geometry, and group theory
Quantum computers can execute algorithms that sometimes dramatically
outperform classical computation. Undoubtedly the best-known example of this is
Shor's discovery of an efficient quantum algorithm for factoring integers,
whereas the same problem appears to be intractable on classical computers.
Understanding what other computational problems can be solved significantly
faster using quantum algorithms is one of the major challenges in the theory of
quantum computation, and such algorithms motivate the formidable task of
building a large-scale quantum computer. This article will review the current
state of quantum algorithms, focusing on algorithms for problems with an
algebraic flavor that achieve an apparent superpolynomial speedup over
classical computation.Comment: 20 pages, lecture notes for 2010 Summer School on Diversities in
Quantum Computation/Information at Kinki Universit
Generating a Quadratic Forms from a Given Genus
Given a non-empty genus in dimensions with determinant , we give a
randomized algorithm that outputs a quadratic form from this genus. The time
complexity of the algorithm is poly; assuming Generalized Riemann
Hypothesis (GRH).Comment: arXiv admin note: text overlap with arXiv:1409.619
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