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After taking linear algebra I decided I could try my hand at learning some introductory QC algorithms, and downloading this introductory paper from arxiv: http://arxiv.org/abs/quant-ph/0301079v1

After mulling through it for a couple of days, I got a little disturbed by their sketchy index finding function at the bottom of page 14, stated as follows:

Erm...'let us assume'? Now define f: {0, ..., N - 1} --> {0,1} as a function which recognizes the solution:

f(i) = 1 if i is the searched element (i0)

f(i0 = 0 otherwise.

This function is used in the classical algorithm. In the quantum algorithm, let us assume that it is possible to build a linear unitary operator also dependent on f, Uf, such that

Uf([i>[j>) = [i>|j+f(i)>

Since the function f(i) can be implemented in a classical computer, I understand that we can decompose this function into AND and NOT gates and turn them into the Toffoli and CNOT quantum equivalents, and thereby apply the function f(i) via quantum gates. But wouldn't the entire database infrastructure have to be..err...in qubits for this to work?

Also, what's stopping me from defining almost any function whatsoever, marking it in the same way, and use Grover's algorithm to find the marked element(s)?

For example, could I replace that function f(i) with my own, say:

f(N,i) = 1 if N%i == 0

f(N, i) = 0 otherwise

[where N = 2^(2*# of qubits) ]

and use it to increase the likelihood of finding prime factors, thereby using Grover's algorithm as an inefficient replacement for Shor's?

I feel like there's something I'm not getting...

Thanks for the help,

M

(Note: sorry for this isn't the right thread for this topic; move if necessary)

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# A Question About Grover's Algorithm (Quantum Computing)

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