Geometric phases and quantum computations
نویسندگان
چکیده
منابع مشابه
Geometric Properties of Quantum Phases
The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the phase. By introducing another connection, the Pancharatnam phase formula is derived following a different procedure.
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In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also introduce a number of examples that will help the reader understand the basic issues involved. In the second part we show how to perform a universal quantum comp...
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Geometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an externally driven quantum system with adiabatic evolution law and finite number of the energy levels. The corresponding evolution operators represent quantum gate...
متن کاملOn geometric phases for quantum trajectories
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by using Uhlmann’s concept of parallel transport along the individual trajectories. We put forward an experimental realization of the geometric phase for a quan...
متن کاملGeometric Classification of Topological Quantum Phases
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a transformation group.
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ژورنال
عنوان ژورنال: Physics Letters A
سال: 2002
ISSN: 0375-9601
DOI: 10.1016/s0375-9601(02)01230-6