A new algorithm for directed quantum search

Quantum searching requires precise knowledge of problem parameters (such as the fraction of target states) for efficient operation. Recently an algorithm has been discovered, referred to as the Phase-π/3 search algorithm, which gets around this limitation. This algorithm can search a database with the fraction of target states equal to 1 − ǫ so that in q queries it produces a probability of error equal to ǫ2q+1 which has since been proved to be optimal. This paper gives a different algorithm which has the same worst-case behavior as the Phaseπ/3 search algorithm but much better average-case behavior. Furthermore the new algorithm gives ǫ2q+1 convergence for all integral q, the Phase-π/3 search algorithm, requires q to be (3n − 1)/2, with n a positive integer. In the new algorithm, the operations are controlled in a special way by two ancilla qubits, and fixed point behavior is achieved by irreversible measurement operations.