I'm wondering how it really is useful.(adsbygoogle = window.adsbygoogle || []).push({});

The input for the, say 2-qubit, quantum computer that is running Grover's algoritm is

[tex]|\Psi \rangle = (|1 \rangle + |2 \rangle + |3 \rangle + |4 \rangle) / \sqrt{4}[/tex]

And let us say we're looking the 3rd element in the so-called database.

Now, Grover operator involves the Oracle operator, which basically negates the sign of the element we're looking for, i.e. sign of [tex]|3 \rangle[/tex], which means [tex]O=I-2 |3 \rangle \langle 3 |[/tex]. The operator can be written in the obvious basis as

[tex]O = \[ \left( \begin{array}{cccc}

1 & 0 & 0 & 0 \\

0 & 1 & 0 & 0 \\

0 & 0 & -1 & 0 \\

0 & 0 & 0 & 1 \\

\end{array} \right)\] [/tex]

And the Grover operator is [tex]G = (2 |\Psi \rangle \langle \Psi | - I) O[/tex]

Anyway, upon acting "enough" on the input state, our output is roughy [tex]|3 \rangle[/tex], i.e.

[tex]|3 \rangle \approx G^n |\Psi \rangle[/tex]

How is this output useful? Other than this, if this is the big result, how come do we use the state [tex]|3 \rangle[/tex] in reaching this result (it was a part of Oracle operator, right?)

I've suddenly started to think it was some sort of a hoax but then it's not, and now I think I'm missing some crucial point, something I fail to see. Please show me how this is a "(unordered) database search"...

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# Grover's Algorithm: is it really a search algorithm

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