  We determine the universal law for fidelity decayin quantum computations of
complex dynamics in presenceof internal static imperfections in a quantum
computer. Our approach is based on random matrix theory applied toquantum
computations in presence of imperfections.The theoretical predictions are
tested and confirmed in extensive numerical simulations of a quantum algorithm
for quantum chaos in the dynamical tent map with up to 18 qubits. The theory
developed determines the time scales forreliable quantum computations in
absence of the quantum error correction codes. These time scales are related to
the Heisenberg time, the Thouless time, and the decay time given by Fermi's
golden rule which are well known in the context of mesoscopic systems. The
comparison is presented for static imperfection effects and random errors in
quantum gates. A new convenientmethod for the quantum computation of the
coarse-grained Wigner function is also proposed.
