Generalized Noiseless Quantum Codes utilizing Quantum Enveloping Algebras

Abstract

A generalization of the results of Rasetti and Zanardi concerning avoiding errors in quantum computers by using states preserved by evolution is presented. The concept of the dynamical symmetry is generalized from the level of classical Lie algebras and groups, to the level of a dynamical symmetry based on quantum Lie algebras and quantum groups (in the sense of Woronowicz). An intrinsic dependence of the concept of dynamical symmetry on the differential calculus (which holds also in the classical case) is stressed. A natural connection between quantum states invariant under a quantum group action, and quantum states preserved by the dynamical evolution is discussed.