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Edited quantum 16

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1 parent b6cb6cd commit bc7a0bd136698bc0e52fe3bad32b084438341e18 @thenoviceoof committed Apr 9, 2012
Showing with 4 additions and 4 deletions.
  1. +4 −4 quantum/16
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@@ -122,15 +122,15 @@ motivation:
--------------------
Proof:
-F|i>
+F|j>
= 1/\sqrt{N} \sum_k e^(2\pi i (j k)/N) |k>
// switch to bitwise k
- = 1/\sqrt{N} \sum_k e^(2\pi i (j (2^n k_1 .. k_n)/2^n)/N) |k_1>..|k_n>
- = 1/\sqrt{N} \sum_k_1 ... \sum_k_n
+ = 1/\sqrt{N} \sum_k e^(2\pi i (j (2^n k_1 + .. + k_n)/2^n)/N) |k_1>..|k_n>
+ = 1/\sqrt{N} \sum_{k_1=0}^1 ... \sum_k_n
e^(2\pi i j k_1/2)..e^(2\pi i j k_n/2^n) |k_1>..|k_n>
= 1/\sqrt{N} \sum_k_1 e^(2\pi i j k_1/2) |k_1> ...
\sum_k_n e^(2\pi i j k_n/2^n) |k_n> ...
- = 1/\sqrt{N} \tensor_l=0^n ( \sum_k_1 e^(2\pi i j k_l/2^l) |k_l> )
+ = 1/\sqrt{N} \tensor_l=0^n ( \sum_{k_l} e^(2\pi i j k_l/2^l) |k_l> )
we got our tensor product form, but we need to interpret it
examples:

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