Extension To Space With Multiple Targets
If, instead of 1 matching entry, there are k matching entries, the same algorithm works but the number of iterations must be π(N/k)1/2/4 instead of πN1/2/4. There are several ways to handle the case if k is unknown. For example, one could run Grover's algorithm several times, with
iterations. For any k, one of iterations will find a matching entry with a sufficiently high probability. The total number of iterations is at most
which is still O(N1/2). It can be shown that this could be improved. If the number of marked items is k, where k is unknown, there is an algorithm that finds the solution in queries. This fact is used in order to solve the collision problem.
Read more about this topic: Grover's Algorithm
Famous quotes containing the words extension, space and/or multiple:
“The desert is a natural extension of the inner silence of the body. If humanity’s language, technology, and buildings are an extension of its constructive faculties, the desert alone is an extension of its capacity for absence, the ideal schema of humanity’s disappearance.”
—Jean Baudrillard (b. 1929)
“With sturdy shoulders, space stands opposing all its weight to nothingness. Where space is, there is being.”
—Friedrich Nietzsche (1844–1900)
“There is a continual exchange of ideas between all minds of a generation. Journalists, popular novelists, illustrators, and cartoonists adapt the truths discovered by the powerful intellects for the multitude. It is like a spiritual flood, like a gush that pours into multiple cascades until it forms the great moving sheet of water that stands for the mentality of a period.”
—Auguste Rodin (1849–1917)