Z.exp_i().to_matrix() disagrees with documented behavior

[jlapeyre]

Z.exp_i().to_matrix() and X.exp_i().to_matrix() give incorrect results.

What is the current behavior?

In [1]: from qiskit.aqua.operators import Z                                                                                                        

In [2]: Z.exp_i().to_matrix()                                                                                                                      
Out[2]: 
array([[1.        +0.j        , 0.        +0.j        ],
       [0.        +0.j        , 0.54030231+0.84147098j]])

What is the expected behavior?

The docs string for exp_i is "Return a CircuitOp equivalent to e^-iH for this operator H", so I expect this matrix:

In [1]: from qiskit.aqua.operators import Z                                                                                                        

In [2]: import scipy                                                                                                                               

In [3]: scipy.linalg.expm(-1j * Z.to_matrix())                                                                                                     
Out[3]: 
array([[0.54030231-0.84147098j, 0.        +0.j        ],
       [0.        +0.j        , 0.54030231+0.84147098j]])

It looks like there are two problems

• Z.exp_i() returns PrimitiveOp(RZGate(1)) which has a spurious (in this case) factor of 1/2 in the phase. https://github.com/Qiskit/qiskit-aqua/blob/38f727b618b0b09a2aaf6deee8ad4e5fda7fb814/qiskit/aqua/operators/primitive_ops/pauli_op.py#L228

• RZGate(2).to_matrix() returns the correct matrix, but PrimitiveOp(RZGate(2)).to_matrix() does not. The latter uses a 'unitary_simulator' to compute the matrix. This includes an additional global phase factor, which may not matter in some cases, but it does here.
  https://github.com/Qiskit/qiskit-aqua/blob/38f727b618b0b09a2aaf6deee8ad4e5fda7fb814/qiskit/aqua/operators/primitive_ops/circuit_op.py#L149

• Qiskit Aqua version:
  c8193ac Aug 13
• Python version:
  3.8.3
• Operating system:
  linux