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:
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“In the United States there is more space where nobody is is than where anybody is.”
—Gertrude Stein (1874–1946)
“Combining paid employment with marriage and motherhood creates safeguards for emotional well-being. Nothing is certain in life, but generally the chances of happiness are greater if one has multiple areas of interest and involvement. To juggle is to diminish the risk of depression, anxiety, and unhappiness.”
—Faye J. Crosby (20th century)