Abstract
We give a representation of the Toffoli gate of -depth one, using four ancillas. More generally, we describe a class of circuits whose -depth can be reduced to one by using sufficiently many ancillas. We show that the cost of adding an additional control to any controlled gate is at most eight additional gates and -depth two. We also show that the circuit does not possess a -depth one representation with an arbitrary number of ancillas initialized to .
- Received 3 October 2012
DOI:https://doi.org/10.1103/PhysRevA.87.042302
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