Investigation Of Geometrical Phase In Quantum Information And Computation Theory

Karimi Dehkordi, Niloofar (2017) Investigation Of Geometrical Phase In Quantum Information And Computation Theory. Masters thesis, University of Mohaghegh Ardabili.

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Abstract

The geometric phase is the comparison the of a physical quantity due to the changes on a closed cruve in the system state space. These phases are experimentally measurable because of, that the space of a time dependent quantum system may be a curveture, therefore the Holonomy arises from this curveture. The Berry phase has three key features, which makes it very important. First, the Berry phase is gauge invariance. Especial functions are defined by aequal linear equation, hence it has a multiplicative guage freedom in a general phase factor independent of the parameter. Berry phase (forget from on phase factor ) with this phase factor remains unchanged provided that the special function is on a single loop value. This makes the Berry phase to be a physical quantity that is experimentally measureable by inter ference phenomena. Secondly, Berry phase is a geometric concept. that’s mean it can be written as a linear integral of loop in parameter space, which does not depend on the rate of change on the loop. This property makes it mesureable the Berry phase in terms of local geometric quantites in the parameter space. In fact, Berry showed that this phase can be written as a find integral (Berry curve) on the surface. Berry curve plays an essential role in effective dynamics with variables with degrees of slow release. Third, the Berry phase is similar to that of guage field and differential geometry theory. This makes beauty, intuition and the same concept in physics.

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