Measurement of an integral of a classical field with a single quantum particle

A method for measuring an integral of a classical field via local interaction of a single quantum particle in a superposition of 2^N states is presented. The method is as efficient as a quantum method with N qubits passing through the field one at a time and it is exponentially better than any known classical method that uses N bits passing through the field one at a time. A related method for searching a string with a quantum particle is proposed.