NonAbelian Berry connections for quantum computation
Abstract
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 nonAbelian 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 multipartite 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.
 Publication:

Physical Review A
 Pub Date:
 December 1999
 DOI:
 10.1103/PhysRevA.61.010305
 arXiv:
 arXiv:quantph/9907103
 Bibcode:
 1999PhRvA..61a0305P
 Keywords:

 03.67.Lx;
 03.65.Fd;
 Quantum computation;
 Algebraic methods;
 Quantum Physics;
 High Energy Physics  Theory
 EPrint:
 5 pages, no figures, revtex, minor changes, version accepted by Phys. Rev A (rapid comm.)