An adiabatic cyclic evolution of control parameters of a quantum system ends
up with a holonomic operation on the system, determined entirely by the
geometry in the parameter space. The operation is given either by a simple
phase factor (a Berry phase) or a non-Abelian unitary operator depending on the
degeneracy of the eigenspace of the Hamiltonian. Geometric quantum computation
is a scheme to use such holonomic operations rather than the conventional
dynamic operations to manipulate quantum states for quantum information
processing. Here we propose a geometric quantum computation scheme which can be
realized with current technology on nanoscale Josephson-junction networks,
known as a promising candidate for solid-state quantum computer.Comment: 6 figures; to appear in J. Phys.: Condens. Mat