Holonomic quantum computation

We show that the notion of generalized Berry phase i.e., non-abelian holonomy, can be used for enabling quantum computation. The computational space is realized by a n-fold degenerate eigenspace of a family of Hamiltonians parametrized by a manifold M. The point of M represents classical configuration of control fields and, for multi-partite systems, couplings between subsystem. Adiabatic loops in the control M induce non trivial unitary transformations on the computational space. For a generic system it is shown that this mechanism allows for universal quantum computation by composing a generic pair of loops in M. (C) 1999 Elsevier Science B.V. All rights reserved.