Geometric Effects and Computation in Spin Networks

Abstract

When initially introduced, a Hamiltonian that realises perfect transfer of a quantum state was found to be analogous to an x-rotation of a large spin. In this paper we extend the analogy further to demonstrate geometric effects by performing rotations on the spin. Such effects can be used to determine properties of the chain, such as its length, in a robust manner. Alternatively, they can form the basis of a spin network quantum computer. We demonstrate a universal set of gates in such a system by both dynamical and geometrical means.