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:I do not understand what you mean by concrete. But as for your direct question. f is a boolean function it outputs 1 or 0 so (-1)^f(x) = -1 when f(x) is 1 and (-1)^f(x)=1 when f(x) is 0. If you're prone to the notation of the basis states |1>, |-1> then the coeficent (-1)^f(x) could be replaced with f(x).
:On to your next question. x is not 0. We are measuring 0. Before the haddamard there are 2^n |x>'s. After the haddamard each |x> is repalced with 2^n |y>'s. The summation is rearranged so that equal |y>'s appear together, ie 2^n |y>'s each with it's own summation as a coefficent. To determine the probability of measuring all qubits zero we plug in y=0 to the |y>=|0> coefficent and calculate the square magnitude. If this argument convinces you please suggest what parts of it we should add to the article. [[User:Skippydo|Skippydo]] 12:17, 9 July 2007 (UTC)
In article is small calculation mistake.
True my Formula is:
:input: <math>x_1, x_2, x_3,..., x_{n-1}, x_n</math>
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