For a n-qubit quantum state $|\psi\rangle=\displaystyle\sum_{i=0}^{2^N-1}|i\rangle$, by definition it's density matrix is $|\psi\rangle\langle\psi|=\displaystyle\sum_{i,j=0}^{2^N-1}|j\rangle\langle i|$.
Recently I am trying to implement a quantum neural network given by a paper, and one step of it is required so, maybe up to a normalization constant(at supplementary note 2, when calculating the derivative).
For a $2^N$ dimensional identity matrix, it does not violate the requirements of being a density matrix, but I just cannot figure out how to do so and I even think this is not possible, have anybody be at this place before?
An additional requirement of mine is that the density matrix must be produced by some qubits or this problem might be truly tedious.