`Isometry` is phase-incorrect for `[-1,0]`

[Cryoris]

Environment

• Qiskit version: 2.3.0rc1 (& others)
• Python version: 3.11
• Operating system: macOS

What is happening?

Isometry does not correctly set the global phase if the input state is the single-qubit $-|0\rangle$, i.e. [-1, 0]. For all other global phases and more than single-qubit states it works, though. This affects Initialize and StatePreparation, too, since they are based on Isometry.

How can we reproduce the issue?

from qiskit.circuit.library import Isometry, Initialize
from qiskit.quantum_info import Statevector
import numpy as np

vecs = [
  [np.exp(1j * np.pi), 0], # -|0>, doesn't work
  [np.exp(1j * np.pi * 0.9999), 0], # close to -|0>, works
  [np.exp(1j * np.pi), 0, 0, 0], # -|00>, works
]

for vec in vecs:
  sv = Statevector(Isometry(vec, 0, 0).definition)
  print(sv)

What should happen?

The output circuit should have the correct phase of pi.

Any suggestions?

Isometry does a bunch of tests checking if matrices are the identity up to global phase. We can probably fix this by correcting the global phase there.

[Kalpeshcodes]

I would like to work on this issue. I was experimenting with this and I believe the issue stems from the following check as bypassing it results in the correct phase.

qiskit/qiskit/circuit/library/generalized_gates/isometry.py

Lines 236 to 240 in dc14dfb

	if not isometry_rs.ucg_is_identity_up_to_global_phase(single_qubit_gates, self._epsilon):
	control_labels = list(range(target_label))
	diagonal_ucg = self._append_ucg_up_to_diagonal(
	circuit, q, single_qubit_gates, control_labels, target_label
	)

It uses the ucg_is_identity_up_to_global_phase function from the Rust implementation isometry_rs. I am still looking into this.