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- Title
Systematic analysis of majorization in quantum algorithms.
- Authors
Orús, R.; Latorre, J.I.; Martín-Delgado, M.A.
- Abstract
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 in- stances 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.
- Subjects
QUANTUM theory; ALGORITHMS; FOURIER transforms; FOURIER analysis; AFFINAL relatives; MATHEMATICAL models
- Publication
European Physical Journal D (EPJ D), 2004, Vol 29, Issue 1, p119
- ISSN
1434-6060
- Publication type
Article
- DOI
10.1140/epjd/e2004-00009-3