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While performing VQE calculations of medium-sized molecules like H2O, using Qiskit AerSimulator with noise, I noticed that even for a large number of shots, the speed of simulation using statevector method is superior to the speed of simulation when using density matrix. While I think everybody with some basic quantum physics training understands how a noisy simulation using a density matrix works, I am confused how this is actually done using a statevector calculation? For example, I noticed that in Qiskit measurement error mitigation is not supported when using statevector simulation. How accurate are the results of statevector simulation in Qiskit are expected to be when compared to a density matrix simulation?

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Trajectory - the simulator draws in random (probability depends on the quantum state and noise) one of the Kraus operators, applies it, and normalizes the state. For a large number of shots, if you construct the density matrix from all the resulting state vectors, it will converge to the true density matrix. But I don't know how fast it will be, I think you'd need a very large number of shots for good convergence.

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