Incorrectly generated matrix out of a list of Pauli strings after converting to opflow

[Brogis1]

Information

• Qiskit Aqua version:
  'qiskit-terra': '0.17.0',
  'qiskit-aer': '0.8.0',
  'qiskit-ignis': '0.6.0',
  'qiskit-ibmq-provider': '0.12.0',
  'qiskit-aqua': '0.9.0'

• Python version:
  Python 3.6.11 | packaged by conda-forge | (default, Aug 5 2020, 20:19:23)

• Operating system:
  macOS Cataline Version 10.15.5 (19F101)

What is the current behavior?

Problem spotted when executed the NumpyEigensolver for an operator.
The matrix and the spectrum of an operator (specific case) is changed when using to_opflow() (automatically called for legacy operators in the NumpyEigensolver).

Steps to reproduce the problem

Given a list of Paulis strings with coefficients in a dictionary (particular case), giving it to WeightedPauliOperator to construct the matrix with qubit_op= WeightedPauliOperator.from_dict(pauli_list) then matrix = to_matrix_operator(qubit_op).dense_matrix upon diagonalization produces correct expected eigenvalues.
Then, when switching to_opflow(), with qubit_op_opflow = qubit_op.to_opflow() then
qubit_op_opflow_matrix = qubit_op_opflow.to_matrix() the matrix and eigenvalues are modified.

from qiskit.aqua.operators import WeightedPauliOperator
import numpy as np
from qiskit.aqua.operators.legacy.op_converter import to_matrix_operator

# Paulis of the operator
h_real_paulis = {'IIII': (4+0j),
 'IIIZ': (3.0025020840279018+0j),
 'IIZI': (0.9974979159720981+0j),
 'IZII': (3.0025020840279018+0j),
 'IZIZ': (1+0j),
 'IZZI': (1+0j),
 'IZZZ': (-0.002502084027901752+0j),
 'XXXX': (1+0j),
 'XXXY': 0.050083375009922104j,
 'XXYX': -0.050083375009922104j,
 'XXYY': (1+0j),
 'XYXX': 0.050083375009922076j,
 'XYYY': 0.050083375009922076j,
 'YXXX': -0.050083375009922076j,
 'YXYY': -0.050083375009922076j,
 'YYXX': (1+0j),
 'YYXY': 0.050083375009922104j,
 'YYYX': -0.050083375009922104j,
 'YYYY': (1+0j),
 'ZIII': (0.9974979159720981+0j),
 'ZIIZ': (1+0j),
 'ZIZI': (0.9999999999999999+0j),
 'ZIZZ': (0.002502084027901752+0j),
 'ZZIZ': (-0.002502084027901752+0j),
 'ZZZI': (0.002502084027901752+0j)}

h_real_paulis_new = {}
h_real_paulis_new['paulis'] = []
for entry, coef in h_real_paulis.items():
    h_real_paulis_new['paulis'].append({"coeff": {"imag": np.imag(coef), "real": np.real(coef)}, "label": entry})

# matrix using Legacy matrix
qubit_op = WeightedPauliOperator.from_dict(h_real_paulis_new)
matrix = to_matrix_operator(qubit_op).dense_matrix
eigs2, eigv2 = np.linalg.eig(matrix)
print(np.sort(eigs2))

# This is also the correct expected spectrum
"""
[-2.00000000e+00 -2.00000000e+00 -1.65685425e+00 -1.11022302e-16
  0.00000000e+00  1.11022302e-16  1.11022302e-16  2.00000000e+00
  2.00000000e+00  6.00000000e+00  6.00000000e+00  8.00000000e+00
  9.65685425e+00  1.00000000e+01  1.00000000e+01  1.60000000e+01]
"""

# matrix after switching to_opflow()
qubit_op_opflow = qubit_op.to_opflow()
qubit_op_opflow_matrix = qubit_op_opflow.to_matrix()
eigs2_opflow, eigv2_opflow = np.linalg.eig(qubit_op_opflow_matrix)
print(np.sort(eigs2_opflow))

# Note the 3rd eigenvalue has changed
"""
[-2.00000000e+00 -2.00000000e+00 -1.68516210e+00 -1.11022302e-16
  0.00000000e+00  1.11022302e-16  1.11022302e-16  2.00000000e+00
  2.00000000e+00  6.00000000e+00  6.00000000e+00  8.00000000e+00
  9.68516210e+00  1.00000000e+01  1.00000000e+01  1.60000000e+01]
"""

What is the expected behavior?

The spectrum of an operator (given as Pauli strings and their coefficients) should not change upon switching to_opflow().

Suggested solutions

Inspect the to_opflow() method and Pauli label to Pauli object converter.

[ikkoham]

Thanks for the issue.
I found that to_opflow() mistakenly converts a imaginary number to a real number.

minimal code

qubit_op = WeightedPauliOperator.from_dict({"paulis":[{"coeff": {"imag": 1, "real": 0}, "label": "X"}]})
print(qubit_op.to_opflow().to_matrix())

This returns a Pauli X.

I will fix this issue.