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ON THE ADIABATIC EVOLUTION OF ONE-DIMENSIONAL PROJECTOR HAMILTONIANS.
- Source :
-
International Journal of Quantum Information . Jun2012, Vol. 10 Issue 4, p-1. 9p. - Publication Year :
- 2012
-
Abstract
- In this paper, we discuss the adiabatic evolution of one-dimensional projector Hamiltonians. Three kinds of adiabatic algorithms for this problem are shown, in which two of them provide a quadratic speedup over the other one. But when the ground state of the initial Hamiltonian and that of the final Hamiltonian have a zero overlap, the algorithms above all fail, in the sense of infinite time complexity. A corresponding revised method for this phenomenon through adding a driving Hamiltonian is also shown, from which a constant time complexity can be gained. But by a simple analysis, we find that the original time complexity for the adiabatic evolution is shifted to implement the driving Hamiltonian, which is supported by several early works in the literature. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02197499
- Volume :
- 10
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- International Journal of Quantum Information
- Publication Type :
- Academic Journal
- Accession number :
- 83879795
- Full Text :
- https://doi.org/10.1142/S0219749912500463