  Mathematical models of quantum computers such as a multidimensional quantum
Turing machine and quantum circuits are described and its relations with
lattice spin models are discussed. One of the main open problems one has to
solve if one wants to build a quantum computer is the decoherence due to the
coupling with the environment. We propose a possible solution of this problem
by using a control of parameters of the system. This proposal is based on the
analysis of the spin-boson Hamiltonian performed in the stochastic limit
approximation.
