Add convenience methods to create PhasedXZ gate from ZYZ decomposition (

#6569)

Co-authored-by: Pavol Juhas <[email protected]>

cirq-core/cirq/ops/phased_x_gate.py

@@ -28,7 +28,7 @@
 
 @value.value_equality(manual_cls=True, approximate=True)
 class PhasedXPowGate(raw_types.Gate):
-    r"""A gate equivalent to $Z^{p} X^t Z^{-p}$.
+    r"""A gate equivalent to $Z^{-p} X^t Z^{p}$ (in time order).
 
     The unitary matrix of `cirq.PhasedXPowGate(exponent=t, phase_exponent=p)` is:
     $$

cirq-core/cirq/ops/phased_x_z_gate.py

@@ -27,7 +27,7 @@
 
 @value.value_equality(approximate=True)
 class PhasedXZGate(raw_types.Gate):
-    r"""A single qubit gate equivalent to the circuit $Z^z Z^{a} X^x Z^{-a}$.
+    r"""A single qubit gate equivalent to the circuit $Z^{-a} X^x Z^{a} Z^z$ (in time order).
 
     The unitary matrix of `cirq.PhasedXZGate(x_exponent=x, z_exponent=z, axis_phase_exponent=a)` is:
     $$
@@ -67,6 +67,22 @@ def __init__(
         self._z_exponent = z_exponent
         self._axis_phase_exponent = axis_phase_exponent
 
+    @classmethod
+    def from_zyz_angles(cls, z0_rad: float, y_rad: float, z1_rad: float) -> 'cirq.PhasedXZGate':
+        """Create a PhasedXZGate from ZYZ angles.
+
+        The returned gate is equivalent to $Rz(z0_rad) Ry(y_rad) Rz(z1_rad)$ (in time order).
+        """
+        return cls.from_zyz_exponents(z0=z0_rad / np.pi, y=y_rad / np.pi, z1=z1_rad / np.pi)
+
+    @classmethod
+    def from_zyz_exponents(cls, z0: float, y: float, z1: float) -> 'cirq.PhasedXZGate':
+        """Create a PhasedXZGate from ZYZ exponents.
+
+        The returned gate is equivalent to $Z^z0 Y^y Z^z1$ (in time order).
+        """
+        return PhasedXZGate(axis_phase_exponent=-z0 + 0.5, x_exponent=y, z_exponent=z0 + z1)
+
     def _canonical(self) -> 'cirq.PhasedXZGate':
         x = self.x_exponent
         z = self.z_exponent

cirq-core/cirq/ops/phased_x_z_gate_test.py

@@ -34,6 +34,30 @@ def test_eq():
     eq.add_equality_group(cirq.PhasedXZGate(x_exponent=1, z_exponent=0, axis_phase_exponent=0))
 
 
+@pytest.mark.parametrize('z0_rad', [-np.pi / 5, 0, np.pi / 5, np.pi / 4, np.pi / 2, np.pi])
+@pytest.mark.parametrize('y_rad', [0, np.pi / 5, np.pi / 4, np.pi / 2, np.pi])
+@pytest.mark.parametrize('z1_rad', [-np.pi / 5, 0, np.pi / 5, np.pi / 4, np.pi / 2, np.pi])
+def test_from_zyz_angles(z0_rad: float, y_rad: float, z1_rad: float) -> None:
+    q = cirq.q(0)
+    phxz = cirq.PhasedXZGate.from_zyz_angles(z0_rad, y_rad, z1_rad)
+    zyz = cirq.Circuit(cirq.rz(z0_rad).on(q), cirq.ry(y_rad).on(q), cirq.rz(z1_rad).on(q))
+    cirq.testing.assert_allclose_up_to_global_phase(
+        cirq.unitary(phxz), cirq.unitary(zyz), atol=1e-8
+    )
+
+
+@pytest.mark.parametrize('z0', [-0.2, 0, 0.2, 0.25, 0.5, 1])
+@pytest.mark.parametrize('y', [0, 0.2, 0.25, 0.5, 1])
+@pytest.mark.parametrize('z1', [-0.2, 0, 0.2, 0.25, 0.5, 1])
+def test_from_zyz_exponents(z0: float, y: float, z1: float) -> None:
+    q = cirq.q(0)
+    phxz = cirq.PhasedXZGate.from_zyz_exponents(z0, y, z1)
+    zyz = cirq.Circuit(cirq.Z(q) ** z0, cirq.Y(q) ** y, cirq.Z(q) ** z1)
+    cirq.testing.assert_allclose_up_to_global_phase(
+        cirq.unitary(phxz), cirq.unitary(zyz), atol=1e-8
+    )
+
+
 def test_canonicalization():
     def f(x, z, a):
         return cirq.PhasedXZGate(x_exponent=x, z_exponent=z, axis_phase_exponent=a)