fix statevector handling global phase (#5239)

Co-authored-by: Matthew Treinish <mtreinish@kortar.org>

qiskit/quantum_info/states/statevector.py

@@ -676,7 +676,7 @@ class Statevector(QuantumState):
             raise QiskitError('{} instruction definition is {}; expected QuantumCircuit'.format(
                 obj.name, type(obj.definition)))
         if obj.definition.global_phase:
-            statevec._data *= np.exp(1j * obj.definition.global_phase)
+            statevec._data *= np.exp(1j * float(obj.definition.global_phase))
         for instr, qregs, cregs in obj.definition:
             if cregs:
                 raise QiskitError(

test/python/quantum_info/states/test_statevector.py

@@ -22,6 +22,7 @@ from numpy.testing import assert_allclose
 from qiskit.test import QiskitTestCase
 from qiskit import QiskitError
 from qiskit import QuantumRegister, QuantumCircuit
+from qiskit import transpile
 from qiskit.circuit.library import HGate
 
 from qiskit.quantum_info.random import random_unitary
@@ -866,6 +867,17 @@ class TestStatevector(QiskitTestCase):
                 expval = psi.expectation_value(op)
                 self.assertAlmostEqual(expval, target)
 
+    def test_global_phase(self):
+        """Test global phase is handled correctly when evolving statevector."""
+
+        qc = QuantumCircuit(1)
+        qc.rz(0.5, 0)
+        qc2 = transpile(qc, basis_gates=['p'])
+        sv = Statevector.from_instruction(qc2)
+        expected = np.array([0.96891242-0.24740396j, 0])
+        self.assertEqual(float(qc2.global_phase), -1/4)
+        self.assertEqual(sv, Statevector(expected))
+
 
 if __name__ == '__main__':
     unittest.main()