Eigenstates of an operating quantum computer: hypersensitivity to static imperfections

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 nq. 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).