  Here is discussed application of the Weyl pair to construction of universal
set of quantum gates for high-dimensional quantum system. An application of Lie
algebras (Hamiltonians) for construction of universal gates is revisited first.
It is shown next, how for quantum computation with qubits can be used
two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford
algebras, and discussed well known applications to product operator formalism
in NMR, Jordan-Wigner construction in fermionic quantum computations. It is
introduced universal set of quantum gates for higher dimensional system
(``qudit''), as some generalization of these models. Finally it is briefly
mentioned possible application of such algebraic methods to design of quantum
processors (programmable gates arrays) and discussed generalization to quantum
computation with continuous variables.
