How to simulate the density matrix in Qiskit when using the qasm simulator?

Question

When simulating a circuit using qasm simulator, if there is a depolarizing channel in the noise model, then the results could be mixed states. How can I calculate the density matrix of the mixed states?

Answer 1

The easiest way to do this would be to probably use the density matrix snapshot instruction: https://qiskit.org/documentation/stubs/qiskit.providers.aer.extensions.SnapshotDensityMatrix.html#qiskit.providers.aer.extensions.SnapshotDensityMatrix basically just add circuit.snapshot_density_matrix('density_matrix') to your circuit where you want to get the density matrix. That will store the density matrix in the output results. Here is an example script:

from qiskit.test.mock import FakeVigo
from qiskit import QuantumCircuit
from qiskit.providers.aer import extensions  # import aer snapshot instructions
from qiskit import execute


qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
qc.snapshot_density_matrix('density_matrix')
result = execute(qc, FakeVigo()).result()
# Extract density matrix snapshot from result object:
density_matrix = result.data()['snapshots']['density_matrix']['density_matrix'][0]['value']
print(density_matrix)

In that script FakeVigo is just running Aer under the covers with a noise model taken from a snapshot of the backend properties from the IBMQ vigo device.