assignment5 - Physics 681-481 CS 483 Assignment#5(please...

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March 16, 2006 Physics 681-481; 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 (post-quantum- 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 ? These numbers are small enough to find with an exhaustive computer search, but you
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