assignment6 - April 6 2006 Physics 681-481 CS 483...

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April 6, 2006 Physics 681-481; CS 483: Assignment #6 Searching for one of 4 items (please hand in after the lecture, Thursday, April 20) We explore here Grover’s algorithm when it is applied to identify one of only four items. This turns out to be a special case in two ways. (1) The probability of success after just a single query of the oracle turns out to be exactly 1. (2) The general procedure for constructing W = 2 | φ ih φ | - 1 out of Toffoli gates does not apply when the input register has only two qubits, and a different (simpler) construction must be used, special to the case | φ i = 1 2 ( | 00 i + | 01 i + | 10 i + | 11 i ) . 1. To convince yourself that Grover’s algorithm is not entirely uninteresting when N = 4, note that if you have a classical oracle that indicates which of four items is special, all you can do is apply the oracle to one randomly selected item after another. What is the mean number of queries of the classical oracle required to determine which item is special?
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