# hw04 - March 3, 2005 Physics 681-481; CS 483: Assignment #4...

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March 3, 2005 Physics 681-481; CS 483: Assignment #4 (please hand in after the lecture, Thursday, March 17th) I. Probabilities for solving Simon’s problem. As described on pages 16-18 of Chapter 2, to estimate how many times a quantum computer has to invoke the subroutine U f to solve Simon’s problem, we must answer a purely mathematical question. We have an n -dimensional space of vectors whose com- ponents are either 0 or 1, on which vector addition and inner products are both carried out with modulo 2 arithmetic. We are interested in the ( n - 1)-dimensional subspace of vectors orthogonal to a given vector a . We have a quantum computer program that gives us a random vector y in that subspace. If we run the program n + x times, what is the probability q that n - 1 of the vectors y will be linearly independent? I argue in Chapter 2 that q = ± 1 - 1 2 2+ x ²± 1 - 1 2 3+ x ² ··· ± 1 - 1 2 n + x ² . (1) (a) Consider the case n = 3, x = 0, and a = 111. There are 4 diFerent y

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## This note was uploaded on 09/28/2008 for the course PHYS 481 taught by Professor Anon during the Spring '05 term at Cornell University (Engineering School).

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hw04 - March 3, 2005 Physics 681-481; CS 483: Assignment #4...

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