Holonomic quantum computation

We show that the notion of generalized Berry phase i.e., non-abelian holono my, can be used for enabling quantum computation. The computational space i s realized by a n-fold degenerate eigenspace of a family of Hamiltonians pa rametrized by a manifold M. The point of M represents classical configurati on of control fields and, for multi-partite systems, couplings between subs ystem. Adiabatic loops in the control M induce non trivial unitary transfor mations on the computational space. For a generic system it is shown that t his mechanism allows for universal quantum computation by composing a gener ic pair of loops in M. (C) 1999 Elsevier Science B.V. All rights reserved.