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Unformatted text preview: March 16, 2006 Physics 681481; CS 483: Assignment #5 (please hand in after the lecture, Thursday, April 6th, in three weeks) The two questions that follow illustrate the mathematics of the final (postquantum computational) stage of Shor’s period finding procedure, as described on pages 17 and 18 of Chapter 3 of the lecture notes. The detective work you are asked to carry out makes use of the theorem, cited in the lecture notes, that if j and r have no common factors, and x is an estimate for the fraction j/r that differs from it by less than 1 / 2 r 2 , then j/r will appear as one of the partial sums in the continued fraction expansion of x . 1. Suppose you know that the integer r is less than 100 and that 11490 is within 1 2 of an integral multiple of 2 14 /r . What is r ? 2. Suppose you know that the integer r is less than 100 and that 11343 and 13653 are both within 1 2 of integral multiples of 2 14 /r . What is r ?...
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This homework help was uploaded on 02/01/2008 for the course CS 483 taught by Professor Ginsparg during the Spring '08 term at Cornell.
 Spring '08
 Ginsparg

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