Use Operator rather than unitary simulator to convert circuit to unit…

…ary matrix (qiskit-community/qiskit-aqua#1224)

* Fix factor of 2 error in converting exp_i to rotation gates

* Make CircuitOp use Operator rather than unitary simulator to get matrix

The unitary simulator does not account for the global phase in a
circuit. qiskit.quantum_info.Operator does account for global phase
when converting (when possible) a circuit to a unitary matrix.

Closes qiskit-community/qiskit-aqua#1218

* Remove note on reversing order of qubits

Using Operator(QuantumCircuit) gives the same qubit ordering
that the previous unitary-simulator-based code did. I removed
the comment entirely because the behavior depends only on
Operator(QuantumCircuit), which is not obscure.

qiskit/aqua/operators/primitive_ops/circuit_op.py

@@ -16,7 +16,8 @@
 import logging
 import numpy as np
 
-from qiskit import QuantumCircuit, BasicAer, execute
+import qiskit
+from qiskit import QuantumCircuit
 from qiskit.circuit.library import IGate
 from qiskit.circuit import Instruction, ParameterExpression
 
@@ -139,14 +140,7 @@ def to_matrix(self, massive: bool = False) -> np.ndarray:
                 ' in this case {0}x{0} elements.'
                 ' Set massive=True if you want to proceed.'.format(2 ** self.num_qubits))
 
-        # NOTE: not reversing qubits!! We generally reverse endianness when converting between
-        # circuit or Pauli representation and matrix representation, but we don't need to here
-        # because the Unitary simulator already presents the endianness of the circuit unitary in
-        # forward endianness.
-        unitary_backend = BasicAer.get_backend('unitary_simulator')
-        unitary = execute(self.to_circuit(),
-                          unitary_backend,
-                          optimization_level=0).result().get_unitary()
+        unitary = qiskit.quantum_info.Operator(self.to_circuit()).data
         # pylint: disable=cyclic-import
         from ..operator_globals import EVAL_SIG_DIGITS
         return np.round(unitary * self.coeff, decimals=EVAL_SIG_DIGITS)

qiskit/aqua/operators/primitive_ops/pauli_op.py

@@ -220,13 +220,13 @@ def exp_i(self) -> OperatorBase:
                 else self.coeff
             # Y rotation
             if corrected_x[sig_qubit_index] and corrected_z[sig_qubit_index]:
-                rot_op = PrimitiveOp(RYGate(coeff))
+                rot_op = PrimitiveOp(RYGate(2 * coeff))
             # Z rotation
             elif corrected_z[sig_qubit_index]:
-                rot_op = PrimitiveOp(RZGate(coeff))
+                rot_op = PrimitiveOp(RZGate(2 * coeff))
             # X rotation
             elif corrected_x[sig_qubit_index]:
-                rot_op = PrimitiveOp(RXGate(coeff))
+                rot_op = PrimitiveOp(RXGate(2 * coeff))
 
             from ..operator_globals import I
             left_pad = I.tensorpower(sig_qubit_index)