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I usually use Qiskit "Aer" to simulate quantum circuit with several methods such as statevector, density_matrix, stabilizer, extended_stabilizer, and matrix_product_state. Recenlty I came across another simulator called "BasicAer" and I wonder if the qiskit BasicAer supports above methods.

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For any provider, you can check the backends with backends():

from qiskit import BasicAer
BasicAer.backends()
[<QasmSimulatorPy('qasm_simulator') from BasicAer()>,
 <StatevectorSimulatorPy('statevector_simulator') from BasicAer()>,
 <UnitarySimulatorPy('unitary_simulator') from BasicAer()>]

Check the doc for each of them:

for backend in BasicAer.backends():
    print("%s: %s" % (backend.name(), backend.__doc__))
qasm_simulator: Python implementation of a qasm simulator.
statevector_simulator: Python statevector simulator.
unitary_simulator: Python implementation of a unitary simulator.
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