Fix global phase in inverse of UCGate (#8508) (#8536)

* Defines the inverse of the global phase

The inverse of UCGate is defined by simply inverting the existing decomposition, but the inverse of the global phase was missing.

* Tests the UCGate.inverse() function

* Lint

* Seed for building the matrices

* Replace `unitary_simulator` by using `qiskit.quantum_info.Operator`.

Co-authored-by: Julien Gacon <gaconju@gmail.com>

* Import `Operator` class

* Release notes

* Lint

* Test the phase of isometry decomposition

* Removes the `prelude` from the release notes file

* Replaces `matrix_equal` with `np.allclose`

Co-authored-by: Julien Gacon <gaconju@gmail.com>
(cherry picked from commit 82c85d8)

Co-authored-by: Israel F. Araujo <israelferrazaraujo@hotmail.com>
Co-authored-by: Jake Lishman <jake.lishman@ibm.com>
Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>

qiskit/extensions/quantum_initializer/uc.py

@@ -110,6 +110,9 @@ def inverse(self):
         definition = QuantumCircuit(*self.definition.qregs)
         for inst in reversed(self._definition):
             definition._append(inst.replace(operation=inst.operation.inverse()))
+
+        definition.global_phase = -self.definition.global_phase
+
         inverse_gate.definition = definition
         return inverse_gate
 

releasenotes/notes/bugfix-ucgate-inverse-global_phase-c9655c13c22e5cf4.yaml

@@ -0,0 +1,9 @@
+---
+fixes:
+  - |
+    Fixes the :meth:`.UCGate.inverse` method which previously did not invert the
+    global phase.
+  - |
+    Fixes the global phase problem of the isometry decomposition. Refer to
+    `#4687 <https://github.com/Qiskit/qiskit-terra/issues/4687>` for more
+    details.

test/python/circuit/test_isometry.py

@@ -24,7 +24,6 @@
 from qiskit import execute
 from qiskit.test import QiskitTestCase
 from qiskit.compiler import transpile
-from qiskit.quantum_info.operators.predicates import matrix_equal
 from qiskit.quantum_info import Operator
 from qiskit.extensions.quantum_initializer.isometry import Isometry
 
@@ -69,7 +68,7 @@ def test_isometry(self, iso):
         unitary = result.get_unitary(qc)
         iso_from_circuit = unitary[::, 0 : 2**num_q_input]
         iso_desired = iso
-        self.assertTrue(matrix_equal(iso_from_circuit, iso_desired, ignore_phase=True))
+        self.assertTrue(np.allclose(iso_from_circuit, iso_desired))
 
     @data(
         np.eye(2, 2),
@@ -108,7 +107,7 @@ def test_isometry_tolerance(self, iso):
         result = execute(qc, simulator).result()
         unitary = result.get_unitary(qc)
         iso_from_circuit = unitary[::, 0 : 2**num_q_input]
-        self.assertTrue(matrix_equal(iso_from_circuit, iso, ignore_phase=True))
+        self.assertTrue(np.allclose(iso_from_circuit, iso))
 
     @data(
         np.eye(2, 2),

test/python/circuit/test_uc.py

@@ -30,6 +30,7 @@
 from qiskit.quantum_info.random import random_unitary
 from qiskit.compiler import transpile
 from qiskit.quantum_info.operators.predicates import matrix_equal
+from qiskit.quantum_info import Operator
 
 _id = np.eye(2, 2)
 _not = np.matrix([[0, 1], [1, 0]])
@@ -71,7 +72,7 @@ def test_ucg(self, squs, up_to_diagonal):
         self.assertTrue(matrix_equal(unitary_desired, unitary, ignore_phase=True))
 
     def test_global_phase_ucg(self):
-        """ "Test global phase of uniformly controlled gates"""
+        """Test global phase of uniformly controlled gates"""
         gates = [random_unitary(2).data for _ in range(2**2)]
         num_con = int(np.log2(len(gates)))
         q = QuantumRegister(num_con + 1)
@@ -85,6 +86,21 @@ def test_global_phase_ucg(self):
 
         self.assertTrue(np.allclose(unitary_desired, unitary))
 
+    def test_inverse_ucg(self):
+        """Test inverse function of uniformly controlled gates"""
+        gates = [random_unitary(2, seed=42 + s).data for s in range(2**2)]
+        num_con = int(np.log2(len(gates)))
+        q = QuantumRegister(num_con + 1)
+        qc = QuantumCircuit(q)
+
+        qc.uc(gates, q[1:], q[0], up_to_diagonal=False)
+        qc.append(qc.inverse(), qc.qubits)
+
+        unitary = Operator(qc).data
+        unitary_desired = np.identity(2**qc.num_qubits)
+
+        self.assertTrue(np.allclose(unitary_desired, unitary))
+
 
 def _get_ucg_matrix(squs):
     return block_diag(*squs)