How to obtain the state vector of a certain number of fixed bits in the output of a multi-bit circuit?

Question

I have a 26 bit output, but I only want to get 8 bit statevector in 26 bit. If I use backend = Aer.get_backend('statevector_simulator') statevector = execute(qc, backend=backend).result().get_statevector(qc), the output is $2^{26}$ outputs, and I want to get $2^8$ output. How can I do in qiskit?

Answer 1

In general, you can't get the state vector for a subset of circuit qubits because they can be entangled with the other qubits. However, you can always use density matrices to represent the state of the qubits (entangled with other qubits or not).

An easy way to get the density matrix for some qubits is to use save_density_matrix method. And if the density matrix represents a pure state, you can use DensityMatrix.to_statevector() method to get the state vector.

As an example, let's create a 5-qubit circuit and get the density matrix of the first two qubits:

circ = QuantumCircuit(5)
circ.h(range(5))
circ.save_density_matrix(qubits=[0, 1]) # <== here
circ.measure_all()

simulator = AerSimulator()
circ = transpile(circ, backend=simulator)
job = simulator.run(circ)
state = job.result().data()['density_matrix']

To display the density matrix:

state.draw('latex')

To get the state vector:

# Check state purity:
if math.isclose(state.purity().real, 1):
    # Get the state vector
    sv = state.to_statevector()

And to display it:

sv.draw('latex')

Answer 2

I think you have to look at this question (and at the 2nd answer in particular): Get state vector of a single qubit in a circuit in Qiskit