# hw03 - Physics 681-481 CS 483 Assignment#3(please hand in...

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February 17, 2005 Physics 681-481; CS 483: Assignment #3 (please hand in after the lecture, Thursday, March 3rd) I. Other aspects of Deutsch’s problem To solve Deutsch’s problem (Chapter 2, Section B) one must apply transformations to the output register as well as the input register before invoking U f to perform the computation. Suppose, though, one only does the standard thing prior to the computation: One starts with the two registers in the state | 0 i| 0 i and applies a Hadamard to the input register. Then the state of the two registers after the action of U f will be | ψ i = 1 2 | 0 i| f (0) i + 1 2 | 1 i| f (1) i , (1) from which, by a direct measurement, one can (randomly) learn the value of f at either 0 or 1. Given two qubits in the state (1) and no information about which of the four possible functions f is, how well can one do in finding out whether or not f (0) = f (1)? There is a way to do this successfully half the time, by making appropriate 1-qubit unitary

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