Monodromy matrices as universal set of quantum gates and dynamics of cold trapped ions

In this paper we describe a feasible construction of universal set of quantum gates using monodromy matrices of Fuchsian system. Fuchsian systems are considered as Schrödinger type equations and it is shown that such quantum systems are exactly solvable. We also show that dynamics of trapped cold ions may be described by a Fuchsian system which also describes the critical points of logarithmic potential associated with equilibrium positions of trapped ions in line geometry. Two different approaches to the inverse problem are also discussed.