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I find it useful to use the Statevector.evolveand DensityMatrix.evolve methods as a shorthand to using the Aer simulators with save_state objects inserted into the circuits, but this approach seems to remove access to the GPU acceleration that Aer can provide. Is there a way to set a GPU backend for the calculation of Statevector.evolveand DensityMatrix.evolve?

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In Qiskit Aer we have AerStatevector. It inherits Statevector. So, you can use it the same way you use Statevector. However, AerStatevector uses same runtime as AerSimulator.

psi = AerStatevector.from_label("00000")
psi.evolve(circuit)

Also, we have AerDensityMatrix which inherits DensityMatrix.

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