I'm looking through Nielson's book on quantum computation and information and in part of it he says that any $C^2(U)$ gate can be constructed from two qubit and one qubit gates. I can't figure out how to do this, or how to verify it (fig 4.8 in his book)(adsbygoogle = window.adsbygoogle || []).push({});

I've attached a photo of the diagram:

http://i.minus.com/i1JWvF4bKP1N1.png [Broken]

Also: Is there an easier way to do this than multipyling 8x8 matricies? Right now I represent the first gate as

[itex] I_1 \otimes\begin{pmatrix}

I & 0 \\

0 & V

\end{pmatrix}_{23}[/itex]

where [itex]I[/itex] is the identity matrix in for one qubit, and [itex]V[/itex] satisfies [itex]V^2 = U[/itex]. [itex]U[/itex] is the unitary matrix being applied.

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# Constructing a Toffoli gate with qubit gates?

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