Slow phase relaxation as a route to quantum computing beyond the quantum chaos border

We reveal that phase memory can be much longer than energy relaxation in systems with exponentially large dimensions of Hilbert space; this finding is documented by 50 years of nuclear experiments, though the information is somewhat hidden. For quantum computers Hilbert spaces of dimension 2100 or larger will be typical and therefore this effect may contribute significantly to reduce the problems of scaling of quantum computers to a useful number of qubits.