Environment

• Qiskit version: 1.1.1
• Python version: 3.11.6
• Operating system: macos

What is happening?

If I understand it right, SparsePauliOp.simplify() does not correctly take into account the phase attribute of its underlying PauliList.

The same also seems true for several SparsePauliOp methods under the header "LinearOp Methods", like conjugate, and adjoint, which update self.coeffs but AFAIK do not look at self.paulis.phase.

(I haven't looked exhaustively for other methods that do not handle paulis.phase.)

How can we reproduce the issue?

For example, define a SparsePauliOp, and then set its paulis attribute to a new value with nonzero phase:

spo = qi.SparsePauliOp(['X', 'X'])
spo.paulis = ['X','-X']
print(spo)

SparsePauliOp(['X', '-X'],
              coeffs=[1.+0.j, 1.+0.j])

So far so good. But now call simplify:

spo.simplify()

SparsePauliOp(['X'],
              coeffs=[2.+0.j])

AFAIK this is incorrect.

What should happen?

The example above should instead match this result where we construct the SPO differently:

spo_2 = qi.SparsePauliOp(['X','-X'])
spo_2.simplify()

SparsePauliOp(['I'],
              coeffs=[0.+0.j])

Any suggestions?

Either we need to fix all the methods to consider paulis.phase, or (probably better) we need to more strictly require that the paulis attribute never has any phase, e.g. updating the paulis() setter to move the phase into the coeffs (don't know what else would need to change).

Another example:

spo_1 = qi.SparsePauliOp(['X'])
spo_1.paulis = qi.PauliList(['-1jX'])
spo_1

SparsePauliOp(['-iX'],
              coeffs=[1.+0.j])

Now try conjugate():

spo_1.conjugate()

SparsePauliOp(['-iX'],
              coeffs=[1.-0.j])