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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!

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  • $\begingroup$ Are you in fact asking for a state preparation routine, or something else? $\endgroup$ Jul 28, 2022 at 14:29
  • $\begingroup$ @Nikita, I am unsure how this can relate to StatePreparation from 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? $\endgroup$ Jul 29, 2022 at 5:50
  • $\begingroup$ I meant that if you are fine with doing the spectral decomposition of $\rho$ yourself, then the question reduces to the state preparation problem for each of the eigenstates, right? What are you looking for, exactly? A function that takes a density matrix and outputs a list of circuits preparing its eigenstates? $\endgroup$ Jul 29, 2022 at 8:03
  • $\begingroup$ Yes, such a function would be very helpful! I was thinking if something like that exists. $\endgroup$ Jul 30, 2022 at 15:48

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