%0 Journal Article
%T Non-Abelian Berry connections for quantum computation
%A Jiannis Pachos
%A Paolo Zanardi
%A Mario Rasetti
%J Physics
%D 1999
%I arXiv
%R 10.1103/PhysRevA.61.010305
%X In the holonomic approach to quantum computation information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible, for a specific model, to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multi-partite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.
%U http://arxiv.org/abs/quant-ph/9907103v2