Modified Grover's algorithm for an expectation value quantum computer

The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are expectation values of observables, is described in detail. A filtering scheme, which effectively determines expectation values on a limited portion of the quantum state, is presented and used to locate a single item for searches involving more than one marked item. A truncated version of Grover's algorithm, requiring fewer steps than the translated standard version but locating marked items just as successfully, is proposed. For quantum computational devices which only return expectation values, the truncated version is superior to its standard counterpart. This indicates that it is possible to modify quantum algorithms so as to reduce the required temporal resources by using the ensemble's spatial resources.