  Classical reversible circuits, acting on $w$~bits, are represented by
permutation matrices of size $2^w \times 2^w$. Those matrices form the group
P($2^w$), isomorphic to the symmetric group {\bf S}$_{2^w}$. The permutation
group P($n$), isomorphic to {\bf S}$_n$, contains cycles with length~$p$,
ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By
Lagrange interpolation between the $p$~matrices of the cycle, we step from a
finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the
unitary group U($n$). As U($2^w$) is the group of all possible quantum
circuits, acting on $w$~qubits, such interpolation is a natural way to step
from classical computation to quantum computation.
