  We propose a classical to quantum information encoding system using
non--orthogonal states and apply it to the problem of searching an element in a
quantum list. We show that the proposed encoding scheme leads to an exponential
gain in terms of quantum resources and, in some cases, to an exponential gain
in the number of runs of the protocol. In the case where the output of the
search algorithm is a quantum state with some particular physical property, the
searched state is found with a single query to the introduced oracle. If the
obtained quantum state must be converted back to classical information, our
protocol demands a number of repetitions that scales polynomially with the
number of qubits required to encode a classical string.

Quantum Physics