This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: March 2, 2006 Physics 681481; CS 483: Assignment #4 (please hand in after the lecture, Thursday, March 16th) I. Probabilities for solving Simons problem. As described on pages 1618 of Chapter 2, to estimate how many times a quantum computer has to invoke the subroutine U f to solve Simons problem, we must answer a purely mathematical question. We have an ndimensional 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 1 1 2 3+ x 1 1 2 n + x . (1) Consider the case n = 3, x = 1, and a = 111. There are 4 different y s (including y = 0) that satisfy...
View Full
Document
 Spring '08
 Ginsparg

Click to edit the document details