Modify definition of readout fidelity in TensoredMeasFitter

[peendebak]

What is the expected behavior?

I have a question on the definition of the readout fidelity for the TensoredMeasFitter (see TensoredMeasFitter docs ). It is defined as the average of the diagonal entries in the individual calibration matrices. But this does not reflect the fidelity of the overall system. This also means the fidelity is not equal to the fidelity we can when we project a full system onto components and then put the components in a TensoredMeasFitter . A minimal example

import itertools
import numpy as np
from qiskit.ignis.mitigation.measurement import CompleteMeasFitter, TensoredMeasFitter

N=3
v=[ [0,1]]*N
state_labels_full = [ ''.join([str(x) for x in t]) for t in itertools.product(*v) ]

full_calibration_matrix=np.array([1])
for ii in range(5):
    A=0.1+.05*np.random.rand(2,2)
    A[0,0]=1-A[0,1]
    A[1,1]=1-A[1,0]
    full_calibration_matrix = np.kron(A, full_calibration_matrix)

print(np.round(full_calibration_matrix, 3))


#print(full_calibration_matrix)

meas_fitter_full = CompleteMeasFitter(None, state_labels=state_labels_full)
meas_fitter_full.cal_matrix = full_calibration_matrix

single_fitters = [meas_fitter_full.subset_fitter([q]) for q in range(N)]


tf=TensoredMeasFitter(results=None, mit_pattern= [ [x] for x in range(N)])
tf.cal_matrices= [s.cal_matrix for s in single_fitters]

print(f'full fitter: fidelity {meas_fitter_full.readout_fidelity():.4f}')

for ii in range(N):
    print(f'subsystem {ii}: fidelity {single_fitters[ii].readout_fidelity():.4f}')
print(f'tensored fitter: fidelity {tf.readout_fidelity():.4f}') # should be equal to the full fitter fidelity?

The output is:

full fitter: fidelity 0.4967
subsystem 0: fidelity 0.6649
subsystem 1: fidelity 0.6696
subsystem 2: fidelity 0.6819
tensored fitter: fidelity 0.6649

Is there a reason for the current definition of the readout fidelity in the TensoredMeasFitter? Or would it be better to refine the fidelity to be more in line with the CompleteMeasFitter?