  In this paper we generalize the usual model of quantum computer to a model in
which the state is an operator of density matrix and the gates are general
superoperators (quantum operations), not necessarily unitary. A mixed state
(operator of density matrix) of n two-level quantum system (open or closed
n-qubit system) is considered as an element of $4^{n}$-dimensional operator
Hilbert space (Liouville space). It allows to use quantum computer (circuit)
model with 4-valued logic. The gates of this model are general superoperators
which act on n-ququats state. Ququat is quantum state in a 4-dimensional
(operator) Hilbert space. Unitary two-valued logic gates and quantum operations
for n-qubit open system are considered as four-valued logic gates acting on
n-ququats. We discuss properties of quantum 4-valued logic gates. In the paper
we study universality for quantum four-valued logic gates.
