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Progress in physics

GEOMETRIC QUANTUM COMPUTATION AND TOPOLOGICAL QUANTUM COMPUTATION——RECENT APPLICATION OF GLOBAL PROPERTIES OF QUANTUM SYSTEMS

Huazhong Li

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The new field of recent developments in quantum computation is reviewed This is an elementary introduction to quantum geometric computation and topological quantum computation.

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We investigate some classes of locally Hamiltonian systems. To formulate a global Hamiltonian formalism a nontrivial principal U(1) bundle over a multi-particle dynamical space is constructed. Lift of dynamics to the total space is considered for the models. Absence of a transposition operator lifting to the bundle space forces us to review a statistics theme from a new standpoint. A topological invariant to characterize system properties is generalized by using geometrical methods and the anyon analogy.
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