Fidelity, quantum computation, and the Wilson Loop

摘要

General properties of quantum systems that interact with a stochastic environment are studied with strong emphasis on the role of physical symmetries. The similarity between the fidelity used to characterize the stability of such a systems and the Wilson loop in QCD is demonstrated, and the fidelity decay rates are derived. The consequences of the existence of a symmetry group on the statistical properties of the system are analyzed for various physical systems: a simple quantum mechanical system, a holonomic quantum computer, and Yang-Mills fields.