I would like to load random quantum states sampled from a given density matrix based on its classical probabilities ie based on the definition of the given density matrix: $\rho = \sum_i p_i |\psi _i \rangle \langle\psi _i|$. An example I am currently trying out is $\rho = 2^{-n}(I_n + \alpha P_n)$ where $I_n$ is the identity matrix, $\alpha$ is a real number say $\in (-1,1)$ and $P_n = \otimes_{i=1}^n P_i$, is a Pauli string. (reference paper)
In qiskit, given such a density matrix how can we obtain the quantum circuit for producing the pure quantum states and the corresponding probabilities for selecting those circuits? Can I give the form of $\rho$ to qiskit and obtain all the $\psi$s ? I could not find anything similar to this in the qiskit documentation on my first try.
PS I understand that $\rho$ is not unique, and one can obtain all the $\psi_i$'s and $p_i$'s trivially by performing a spectral decomposition of $\rho$. But is it possible to generate the quantum circuits that produce such $\psi_i$'s directly?
Thank you in advance!
StatePreparationfrom qiskit. Given the form of $rho$, I would like to obtain circuits (or indirectly prepare the states) that can produce $\psi$s. Is there any documentation available on this at qiskit? $\endgroup$