Given a $0-1$ $2^n*2^n$ matrix, each row has only one 1 each column has only one 1. Such an unitary matrix can be described by an invertible function $f(x) : [1,2^n]\rightarrow [1,2^n]$, Given such a matrix or such a function.
Is there a common way to construct a quantum circuit to implement such an unitary matrix?
