808,067 research outputs found
Systematic Analysis of Majorization in Quantum Algorithms
Motivated by the need to uncover some underlying mathematical structure of
optimal quantum computation, we carry out a systematic analysis of a wide
variety of quantum algorithms from the majorization theory point of view. We
conclude that step-by-step majorization is found in the known instances of fast
and efficient algorithms, namely in the quantum Fourier transform, in Grover's
algorithm, in the hidden affine function problem, in searching by quantum
adiabatic evolution and in deterministic quantum walks in continuous time
solving a classically hard problem. On the other hand, the optimal quantum
algorithm for parity determination, which does not provide any computational
speed-up, does not show step-by-step majorization. Lack of both speed-up and
step-by-step majorization is also a feature of the adiabatic quantum algorithm
solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum
algorithm for the hidden affine function problem does not make use of any
entanglement while it does obey majorization. All the above results give
support to a step-by-step Majorization Principle necessary for optimal quantum
computation.Comment: 15 pages, 14 figures, final versio
An Overview of LISA Data Analysis Algorithms
The development of search algorithms for gravitational wave sources in the
LISA data stream is currently a very active area of research. It has become
clear that not only does difficulty lie in searching for the individual
sources, but in the case of galactic binaries, evaluating the fidelity of
resolved sources also turns out to be a major challenge in itself. In this
article we review the current status of developed algorithms for galactic
binary, non-spinning supermassive black hole binary and extreme mass ratio
inspiral sources. While covering the vast majority of algorithms, we will
highlight those that represent the state of the art in terms of speed and
accuracy.Comment: 21 pages. Invited highlight article appearing in issue 01 of
Gravitational Waves Notes, "GW Notes", edited by Pau Amaro-Seoane and Bernard
F. Schutz at: http://brownbag.lisascience.org/lisa-gw-notes
- …