  The possibility to save and process information in fundamentally
indistinguishable states is the quantum mechanical resource that is not
encountered in classical computing. I demonstrate that, if energy constraints
are imposed, this resource can be used to accelerate information-processing
without relying on entanglement or any other type of quantum correlations. In
fact, there are computational problems that can be solved much faster, in
comparison to currently used classical schemes, by saving intermediate
information in nonorthogonal states of just a single qubit. There are also
error correction strategies that protect such computations.
