Support decomposition of parameterized gates in cirq.PhasedXPowGate (quantumlib#5083)

- Adds support for decomposing parameterized `cirq.PhasedXPowGate`s.
- Also modifies the decomposition to respect global phase, so that the decomposition is valid for controlled variants as well. 
- Part of quantumlib#4858

Author: tanujkhattar

cirq/ops/phased_x_gate.py

@@ -80,9 +80,7 @@ def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
         assert len(qubits) == 1
         q = qubits[0]
         z = cirq.Z(q) ** self._phase_exponent
-        x = cirq.X(q) ** self._exponent
-        if protocols.is_parameterized(z):
-            return NotImplemented
+        x = cirq.XPowGate(exponent=self._exponent, global_shift=self.global_shift).on(q)
         return z ** -1, x, z
 
     @property

cirq/ops/phased_x_gate_test.py

@@ -35,14 +35,11 @@
     ],
 )
 def test_phased_x_consistent_protocols(phase_exponent):
-    # If there is no global_shift, the gate is global phase insensitive.
     cirq.testing.assert_implements_consistent_protocols(
         cirq.PhasedXPowGate(phase_exponent=phase_exponent, exponent=1.0),
-        ignoring_global_phase=False,
     )
     cirq.testing.assert_implements_consistent_protocols(
         cirq.PhasedXPowGate(phase_exponent=phase_exponent, exponent=1.0, global_shift=0.1),
-        ignoring_global_phase=True,
     )
 
 
@@ -171,26 +168,36 @@ def test_str_repr():
     )
 
 
-@pytest.mark.parametrize('resolve_fn', [cirq.resolve_parameters, cirq.resolve_parameters_once])
-def test_parameterize(resolve_fn):
+@pytest.mark.parametrize(
+    'resolve_fn, global_shift', [(cirq.resolve_parameters, 0), (cirq.resolve_parameters_once, 0.1)]
+)
+def test_parameterize(resolve_fn, global_shift):
     parameterized_gate = cirq.PhasedXPowGate(
-        exponent=sympy.Symbol('a'), phase_exponent=sympy.Symbol('b')
+        exponent=sympy.Symbol('a'), phase_exponent=sympy.Symbol('b'), global_shift=global_shift
     )
     assert cirq.pow(parameterized_gate, 5) == cirq.PhasedXPowGate(
-        exponent=sympy.Symbol('a') * 5, phase_exponent=sympy.Symbol('b')
-    )
-    assert (
-        cirq.decompose_once_with_qubits(parameterized_gate, [cirq.LineQubit(0)], NotImplemented)
-        is NotImplemented
+        exponent=sympy.Symbol('a') * 5, phase_exponent=sympy.Symbol('b'), global_shift=global_shift
     )
     assert cirq.unitary(parameterized_gate, default=None) is None
     assert cirq.is_parameterized(parameterized_gate)
+    q = cirq.NamedQubit("q")
+    parameterized_decomposed_circuit = cirq.Circuit(cirq.decompose(parameterized_gate(q)))
+    for resolver in cirq.Linspace('a', 0, 2, 10) * cirq.Linspace('b', 0, 2, 10):
+        resolved_gate = resolve_fn(parameterized_gate, resolver)
+        assert resolved_gate == cirq.PhasedXPowGate(
+            exponent=resolver.value_of('a'),
+            phase_exponent=resolver.value_of('b'),
+            global_shift=global_shift,
+        )
+        np.testing.assert_allclose(
+            cirq.unitary(resolved_gate(q)),
+            cirq.unitary(resolve_fn(parameterized_decomposed_circuit, resolver)),
+            atol=1e-8,
+        )
 
-    resolver = cirq.ParamResolver({'a': 0.1, 'b': 0.2})
-    resolved_gate = resolve_fn(parameterized_gate, resolver)
-    assert resolved_gate == cirq.PhasedXPowGate(exponent=0.1, phase_exponent=0.2)
-
-    unparameterized_gate = cirq.PhasedXPowGate(exponent=0.1, phase_exponent=0.2)
+    unparameterized_gate = cirq.PhasedXPowGate(
+        exponent=0.1, phase_exponent=0.2, global_shift=global_shift
+    )
     assert not cirq.is_parameterized(unparameterized_gate)
     assert cirq.is_parameterized(unparameterized_gate ** sympy.Symbol('a'))
     assert cirq.is_parameterized(unparameterized_gate ** (sympy.Symbol('a') + 1))