30 lines
729 B
Markdown
30 lines
729 B
Markdown
Another well known quantum algorithm for searching.
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Takes a function $f : \{0,1\}^n \rightarrow \{0,1\}$ where f(x) = 1 for exactly one x.
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The goal is to find x.
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New gates: $V_f$ and FLIP$_*$
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$\ket{*}$ denotes the superposition over al classical possibilities.
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### Oracle $V_f$
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![[Pasted image 20260805102238.png]]
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We use the Unitary $U_f$ as previously defined to construct $V_f$
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![[Pasted image 20260805102605.png]]
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### FLIP$_*$
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We first need FLIP$_0$ defined as follows:
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![[Pasted image 20260805102659.png]]
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This is implemented via this circuit:
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![[Pasted image 20260805102717.png]]
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Z is a Pauli matrix and the empty circles denote negative control wires.
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So Z is only applied if all other wires are $\ket{0}$
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