Fix Trotter evolution of sums with identity terms (qiskit-community/q…

…iskit-aqua#1304)

* Fix Trotter evolution of sums with identity terms

Previously, Trotterization did not exclude any terms consisting of a scalar times the
identity from the list of terms to be repeated. Instead, if present, an identity term was
included in the resulting circuit as repeated identity gates, with the coefficient of the
identity operator discarded.  But, this coefficient must be accounted for: exp(-i * coeff
* I) should introduce a global phase.

With this PR, we remove the scalar-multiple-of-identity terms from the SummedOp to be
Trotterized. We then set the global phase of the resulting circuit to account for the
removed identity term.

Fixes qiskit-community/qiskit-aqua#1269

* Add test for Trotter evolution of sums with identity terms

* Add release note for fix-trotter-global-phase

* Fix linter complaints

Co-authored-by: Steve Wood <40241007+woodsp-ibm@users.noreply.github.com>

qiskit/aqua/operators/evolutions/pauli_trotter_evolution.py

@@ -115,8 +115,20 @@ def _recursive_convert(self, operator: OperatorBase) -> OperatorBase:
                 # if operator.primitive.abelian:
                 #     return self.evolution_for_abelian_paulisum(operator.primitive)
                 # else:
-                trotterized = self.trotter.convert(operator.primitive)
-                return self._recursive_convert(trotterized)
+                # Collect terms that are not the identity.
+                oplist = [x for x in operator.primitive if not isinstance(x, PauliOp)
+                          or sum(x.primitive.x + x.primitive.z) != 0]  # type: ignore
+                # Collect the coefficients of any identity terms,
+                # which become global phases when exponentiated.
+                identity_phases = [x.coeff for x in operator.primitive if isinstance(x, PauliOp)
+                                   and sum(x.primitive.x + x.primitive.z) == 0]  # type: ignore
+                # Construct sum without the identity operators.
+                new_primitive = SummedOp(oplist, coeff=operator.primitive.coeff)
+                trotterized = self.trotter.convert(new_primitive)
+                circuit_no_identities = self._recursive_convert(trotterized)
+                # Set the global phase of the QuantumCircuit to account for removed identity terms.
+                circuit_no_identities.primitive.global_phase = -sum(identity_phases)  # type: ignore
+                return circuit_no_identities
             elif isinstance(operator.primitive, PauliOp):
                 return self.evolution_for_pauli(operator.primitive)
             # Covers ListOp, ComposedOp, TensoredOp