Abstract
In this paper we consider circuit synthesis for $n$-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with $O\left(n^2\right)$ gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as $O\left(n^2/\log\, n\right)$ gates.
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