Abstract: As searching targets in an unordered database with Grover's algorithm, difference in marked items is not taken into consideration. If fraction of marked items is greater than 1/4, success probability of search decreases rapidly with increase of marked items. When the fraction of marked items is greater than 1/2, the algorithm is disabled. Aiming at above problems, an improved Grover's algorithm with weighted targets is proposed in which every target is assigned a weight coefficient according to its significance. With these weight coefficients, targets are represented as quantum superpositions which make probability getting target equal to its weight coefficient. An adaptive phase matching method is proposed based on weighted targets. The directions of phase rotations are contrary, and amplitudes of the two phase rotations are determined by inner-product of target quantum superposition and initial state of the system. As the inner-product is greater than ((3-√5)/8)^1/2, success probability is equal to 1 with two steps of Grover iteration at most. The improved quantum searching algorithm and the new phase matching are verified by an example.

Key words: quantum computing, quantum searching, Grover's algorithm, weighted targets, phase matching