  We study the properties of eigenstates of an operating quantum computer which
simulates the dynamical evolution in the regime of quantum chaos. Even if the
quantum algorithm is polynomial in number of qubits $n_q$, it is shown that the
ideal eigenstates become mixed and strongly modified by static imperfections
above a certain threshold which drops exponentially with $n_q$. Above this
threshold the quantum eigenstate entropy grows linearly with $n_q$ but the
computation remains reliable during a time scale which is polynomial in the
imperfection strength and in $n_q$.
