Quantum circuits of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>T</mml:mi></mml:math>-depth one 论文

摘要

We give a $\text{Clifford}+T$ representation of the Toffoli gate of $T$-depth one, using four ancillas. More generally, we describe a class of circuits whose $T$-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 $T$ gates and $T$-depth two. We also show that the circuit $THT$ does not possess a $T$-depth one representation with an arbitrary number of ancillas initialized to $|0\ensuremath{\rangle}$.