Difference between revisions of "Meeting notes 11 05 12"
From Quantum Computing Theory Group
(Created page with "Boolean function $f:Z_2^n \rightarrow R$ Fourier transform") |
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| − | + | Aram | |
| − | + | Real valued function on the boolean hypercube: | |
| + | <math>f:Z_2^n \rightarrow R</math> | ||
| + | This has a the Fourier transform | ||
| + | <math>\hat{f}(y) = {1 \over 2^n} \sum_{x \in Z_2^n} (-1)^{x \cdt y} f(x)</math> | ||
| − | + | ||
| + | flip a random subset of k bits | ||
| + | |||
| + | |||
| + | |y-x|=k | ||
| + | |||
| + | K_k^n(|y|) | ||
| + | |||
| + | Krawtchouck polynomial | ||
| + | http://mathworld.wolfram.com/KrawtchoukPolynomial.html | ||
Revision as of 18:20, 12 May 2011
Aram
Real valued function on the boolean hypercube: <math>f:Z_2^n \rightarrow R</math> This has a the Fourier transform <math>\hat{f}(y) = {1 \over 2^n} \sum_{x \in Z_2^n} (-1)^{x \cdt y} f(x)</math>
flip a random subset of k bits
|y-x|=k
K_k^n(|y|)
Krawtchouck polynomial http://mathworld.wolfram.com/KrawtchoukPolynomial.html
