hw07 - April 21, 2005 Physics 681-481; CS 483: Assignment...

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Unformatted text preview: April 21, 2005 Physics 681-481; CS 483: Assignment #7 (please hand in after the lecture, Thursday, May 5) This is the final assignment. 1. Suppose the only kinds of errors that one had to worry about were one-qubit bit-flip (i.e. X i ) errors. (a) Make an argument like the one given in Chapter 5 for the 5-qubit code, that there is an n for which the dimension of the n-qubit state space is just large enough to accomodate mutually orthogonal two-dimensional subspaces for the uncorrupted and all the corrupted code words. What is that n ? (b) Show for the n you found in (a) that there is indeed an n-qubit code that corrects all bit-flip errors, by writing down the states that encode | i and | 1 i , and writing down a set of commuting hermitian operators whose squares are unity, that preserve both codewords, and have distinct patterns of commutations or anticommutations with each of the operators associated with all the one-qubit bit-flip errors....
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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.

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