I'm working on a project in which I have to find stabilizer states based on a few criteria, the main one being that it has to have a certain amount of coherence, I'm using the following equation to calculate my coherence based on the density matrix of the state. $$ C_r(\rho) = S_{VN}(\rho_{diag}) - S_{VN}(\rho) $$
Where S is the Von Neumann entropy and rho diag is the matrix with the main diagonal equal the density matrix's main diagonal, and every other term is zero. I'm also defining this to be a 5-qubit stabilizer state.
I'm using python and qutip to do these calculations.
Is there a better-than-brute-force algorithm to generate stabilizer states? Is there a way to generate stabilizer states at random based on some criteria?