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: April 20, 2006 Physics 681481; CS 483: Assignment #7 (please hand in after the lecture, Thursday, May 4) This is the final assignment. 1. Suppose the only kinds of errors one had to worry about were bitflip errors, but one wanted to take into account not only single bitflips ( X i ) in the code words but also double bitflips ( X i X j , i 6 = j ). (a) Show that there is an n for which the dimension of the nQbit state space is just large enough to accomodate mutually orthogonal twodimensional subspaces for the uncor rupted code words and all code words suffering either single or double bitflip corruptions. What is that n ? (b) Show for the n you found in (a) that there is indeed a perfect nQbit code that corrects all single and double bitflip 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 (show this explicitly) with each of the operators associated with all the single and double...
View
Full
Document
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 University (Engineering School).
 Spring '08
 Ginsparg

Click to edit the document details