  We introduce an approach for quantum computing in continuous time based on
the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain
conditions, for the design of quantum algorithms running on a nonadiabatic
regime. We show that the relaxation of adiabaticity can be achieved by
processing information in the eigenlevels of a time dependent observable,
namely, the dynamic invariant operator. Moreover, we derive the conditions for
which the computation can be implemented by time independent as well as by
adiabatically varying Hamiltonians. We illustrate our results by providing the
implementation of both Deutsch-Jozsa and Grover algorithms via dynamic
invariants.
