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