How to get statevector of qubits after running quantum circuits on IBMQ real hardware to calculate the fidelity of all qubits individually?

Question

Is it possible to get the statevector while running quantum circuits on IBMQ real hardware? If getting the statevector is not possible can I still calculate the fidelity of a qubit somehow?. What I want is to calculate the fidelity of q0, q1 and q2 in the following circuit after running it on real quantum hardware.

The code I am using is as follows:

import numpy as np
from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister
from qiskit import IBMQ, Aer, transpile, assemble
from qiskit.visualization import plot_histogram, plot_bloch_multivector, array_to_latex
from qiskit.extensions import Initialize
from qiskit.tools.monitor import job_monitor
from qiskit.quantum_info import random_statevector,partial_trace,state_fidelity
from math import pi, sqrt
from qiskit import IBMQ, transpile
from qiskit import IBMQ


IBMQ.load_account()
IBMQ.providers()
provider = IBMQ.get_provider(hub='ibm-q')  # replace by your runtime provider
backend = provider.get_backend('ibmq_lima')
psi= random_statevector(2)
fidelityQ00=[]

# Display it nicely
display(array_to_latex(psi, prefix="|\\psi\\rangle ="))
# Show it on a Bloch sphere
plot_bloch_multivector(psi)

qc = QuantumCircuit(3)
qc.initialize(psi, 0)

qc.u(np.arccos(1/sqrt(5)), 0,0,1)
qc.cx(1,2)
qc.u(np.arccos(sqrt(5)/3), 0,0,2)
qc.cx(2,1)
qc.u(np.arccos(2/sqrt(5)), 0,0,1)
qc.cx(0,1)
qc.cx(0,2)
qc.cx(1,0)
qc.cx(2,0)
qc.draw(output='mpl')
#qc.save_statevector()


#t_qc = transpile(qc, backend, optimization_level=3)
#job = backend.run(t_qc)
#job_monitor(job)
#exp_result = job.result()
#exp_counts = exp_result.get_statevector(qc)


  

Answer 1

I’m almost sure that results from real devices will be in the form of counts so you can’t turn that into a statevector. Each shot of the experiment will end up in a different statevector after all.

But if you want to compare fidelity between count distributions you can use this: https://qiskit.org/documentation/stubs/qiskit.quantum_info.hellinger_fidelity.html