diff --git a/cirq-ionq/cirq_ionq/ionq_native_gates.py b/cirq-ionq/cirq_ionq/ionq_native_gates.py
index e9313b0c43a..80eb49df6aa 100644
--- a/cirq-ionq/cirq_ionq/ionq_native_gates.py
+++ b/cirq-ionq/cirq_ionq/ionq_native_gates.py
@@ -25,18 +25,18 @@
 
 @cirq.value.value_equality
 class GPIGate(cirq.Gate):
-    """The GPI gate is a single qubit gate.
+    r"""The GPI gate is a single qubit gate.
     The unitary of this gate is
-        [[0, e^{-i\\phi}],
-         [e^{-i\\phi}, 0]]
+        [[0, e^{-i*2*\pi*\phi}],
+         [e^{-i*2*\pi*\phi}, 0]]
     """
 
     def __init__(self, *, phi):
         self.phi = phi
 
     def _unitary_(self) -> np.ndarray:
-        top = cmath.exp(self.phi * 1j)
-        bot = cmath.exp(-self.phi * 1j)
+        top = cmath.exp(self.phi * 2 * math.pi * 1j)
+        bot = cmath.exp(-self.phi * 2 * math.pi * 1j)
         return np.array([[0, top], [bot, 0]])
 
     def __str__(self) -> str:
@@ -67,10 +67,10 @@ def _circuit_diagram_info_(
 GPI = GPIGate(phi=0)
 document(
     GPI,
-    """The GPI gate is a single qubit gate.
+    r"""The GPI gate is a single qubit gate.
     The unitary of this gate is
-        [[0, e^{-i\\phi}],
-         [e^{-i\\phi}, 0]]
+        [[0, e^{-i*2*\pi*\phi}],
+         [e^{-i*2*\pi*\phi}, 0]]
     It is driven by Rabi laser.
     https://ionq.com/best-practices
     """,
@@ -79,18 +79,18 @@ def _circuit_diagram_info_(
 
 @cirq.value.value_equality
 class GPI2Gate(cirq.Gate):
-    """The GPI2 gate is a single qubit gate.
+    r"""The GPI2 gate is a single qubit gate.
     The unitary of this gate is
-        \\frac{1}{/\\sqrt{2}}[[1, -i*e^{-i\\phi}],
-         [-i*e^{-i\\phi}, 1]]
+        \frac{1}{/\sqrt{2}}[[1, -i*e^{-i\phi}],
+         [-i*e^{-i\phi}, 1]]
     """
 
     def __init__(self, *, phi):
         self.phi = phi
 
     def _unitary_(self) -> np.ndarray:
-        top = -1j * cmath.exp(self.phase * -1j)
-        bot = -1j * cmath.exp(self.phase * 1j)
+        top = -1j * cmath.exp(self.phase * 2 * math.pi * -1j)
+        bot = -1j * cmath.exp(self.phase * 2 * math.pi * 1j)
         return np.array([[1, top], [bot, 1]]) / math.sqrt(2)
 
     @property
@@ -121,10 +121,10 @@ def _value_equality_values_(self) -> Any:
 GPI2 = GPI2Gate(phi=0)
 document(
     GPI2,
-    """The GPI2 gate is a single qubit gate.
+    r"""The GPI2 gate is a single qubit gate.
     The unitary of this gate is
-        \\frac{1}{/\\sqrt{2}}[[1, -i*e^{-i\\phi}],
-         [-i*e^{-i\\phi}, 1]]
+        \frac{1}{/\sqrt{2}}[[1, -i*e^{-i*2*\pi*\phi}],
+         [-i*e^{-i*2*\phi}, 1]]
     It is driven by Rabi laser.
     https://ionq.com/best-practices
     """,
@@ -133,32 +133,36 @@ def _value_equality_values_(self) -> Any:
 
 @cirq.value.value_equality
 class MSGate(cirq.Gate):
-    """The MS gate is a 2 qubit gate.
+    r"""The MS gate is a 2 qubit gate.
     The unitary of this gate is
-         MS(\\phi_1 - \\phi_0) =
-         MS(t) =
-            \\frac{1}{\\sqrt{2}}
-            [[\\cos(t), 0, 0, -i*\\sin(t)],
-             [0, \\cos(t), -i*\\sin(t), 0],
-             [0, -i*\\sin(t), \\cos(t), 0],
-             [-i*\\sin(t), 0, 0, \\cos(t)]]
+        MS(\phi_0, \phi_1) q_0, q_1 =
+            \frac{1}{\sqrt{2}}
+               [[1, 0, 0, -i*e^{-i*2*\pi*(\phi_0+\phi_1}],
+                [0, 1, -i*e^{-i*2*\pi*(\phi_0-\phi_1}, 0],
+                [0, -i*e^{i*2*\pi*(\phi_0-\phi_1}, 1, 0],
+                [-i*e^{i*2*\pi*(\phi_0+\phi_1}, 0, 0, 1]]
     """
 
-    def __init__(self, *, phi1, phi2):
+    def __init__(self, *, phi0, phi1):
+        self.phi0 = phi0
         self.phi1 = phi1
-        self.phi2 = phi2
 
     def _unitary_(self) -> np.ndarray:
-        tee = self.phi2 - self.phi1
-        diag = math.cos(tee)
-        adiag = -1j * math.sin(tee)
+        diag = 1 / math.sqrt(2)
+        phi0 = self.phi0
+        phi1 = self.phi1
         return np.array(
-            [[diag, 0, 0, adiag], [0, diag, adiag, 0], [0, adiag, diag, 0], [adiag, 0, 0, diag]]
+            [
+                [diag, 0, 0, diag * -1j * cmath.exp(-1j * 2 * math.pi * (phi0 + phi1))],
+                [0, diag, diag * -1j * cmath.exp(-1j * 2 * math.pi * (phi0 - phi1)), 0],
+                [0, diag * -1j * cmath.exp(1j * 2 * math.pi * (phi0 - phi1)), diag, 0],
+                [diag * -1j * cmath.exp(1j * 2 * math.pi * (phi0 + phi1)), 0, 0, diag],
+            ]
         )
 
     @property
     def phases(self) -> Sequence[float]:
-        return [self.phi1, self.phi2]
+        return [self.phi0, self.phi1]
 
     def __str__(self) -> str:
         return 'MS'
@@ -172,27 +176,27 @@ def _circuit_diagram_info_(
         return protocols.CircuitDiagramInfo(wire_symbols=('MS',), exponent=self.phases)
 
     def __repr__(self) -> str:
-        return f'cirq_ionq.MSGate(phi1={self.phi1!r}, phi2={self.phi2!r})'
+        return f'cirq_ionq.MSGate(phi0={self.phi0!r}, phi1={self.phi1!r})'
 
     def _json_dict_(self) -> Dict[str, Any]:
-        return cirq.obj_to_dict_helper(self, ['phi1', 'phi2'])
+        return cirq.obj_to_dict_helper(self, ['phi0', 'phi1'])
 
     def _value_equality_values_(self) -> Any:
-        return (self.phi1, self.phi2)
+        return (self.phi0, self.phi1)
 
 
-MS = MSGate(phi1=0, phi2=0)
+MS = MSGate(phi0=0, phi1=0)
 document(
     MS,
-    """The MS gate is a 2 qubit gate.
+    r"""The MS gate is a 2 qubit gate.
     The unitary of this gate is
-         MS(\\phi_1 - \\phi_0) =
-         MS(t) =
-            \\frac{1}{\\sqrt{2}}
-            [[\\cos(t), 0, 0, -i*\\sin(t)],
-             [0, \\cos(t), -i*\\sin(t), 0],
-             [0, -i*\\sin(t), \\cos(t), 0],
-             [-i*\\sin(t), 0, 0, \\cos(t)]]
+    .. math::
+        MS(\phi_0, \phi_1) q_0, q_1 =
+            \frac{1}{\sqrt{2}}
+               [[1, 0, 0, -i*e^{-i*(\phi_0+\phi_1}],
+                [0, 1, -i*e^{-i*(\phi_0-\phi_1}, 0],
+                [0, -i*e^{i*(\phi_0-\phi_1}, 1, 0],
+                [-i*e^{i*(\phi_0+\phi_1}, 0, 0, 1]]
 
     https://ionq.com/best-practices
     """,
diff --git a/cirq-ionq/cirq_ionq/ionq_native_gates_test.py b/cirq-ionq/cirq_ionq/ionq_native_gates_test.py
index 7e7dd425c7a..5cb98b27469 100644
--- a/cirq-ionq/cirq_ionq/ionq_native_gates_test.py
+++ b/cirq-ionq/cirq_ionq/ionq_native_gates_test.py
@@ -21,7 +21,7 @@
 
 
 @pytest.mark.parametrize(
-    "gate,nqubits", [(GPIGate(phi=0.1), 1), (GPI2Gate(phi=0.2), 1), (MSGate(phi1=0.1, phi2=0.2), 2)]
+    "gate,nqubits", [(GPIGate(phi=0.1), 1), (GPI2Gate(phi=0.2), 1), (MSGate(phi0=0.1, phi1=0.2), 2)]
 )
 def test_gate_methods(gate, nqubits):
     assert str(gate) != ""
@@ -30,7 +30,7 @@ def test_gate_methods(gate, nqubits):
     assert cirq.protocols.circuit_diagram_info(gate) is not None
 
 
-@pytest.mark.parametrize("gate", [GPIGate(phi=0.1), GPI2Gate(phi=0.2), MSGate(phi1=0.1, phi2=0.2)])
+@pytest.mark.parametrize("gate", [GPIGate(phi=0.1), GPI2Gate(phi=0.2), MSGate(phi0=0.1, phi1=0.2)])
 def test_gate_json(gate):
     g_json = cirq.to_json(gate)
     assert cirq.read_json(json_text=g_json) == gate
@@ -59,7 +59,7 @@ def test_gpi2_unitary(phase):
 )
 def test_ms_unitary(phases):
     """Tests that the MS gate is unitary."""
-    gate = MSGate(phi1=phases[0], phi2=phases[1])
+    gate = MSGate(phi0=phases[0], phi1=phases[1])
 
     mat = cirq.protocols.unitary(gate)
     numpy.testing.assert_array_almost_equal(mat.dot(mat.conj().T), numpy.identity(4))
diff --git a/cirq-ionq/cirq_ionq/json_test_data/MSGate.json b/cirq-ionq/cirq_ionq/json_test_data/MSGate.json
index 4b2268733a4..24eea58ec5a 100644
--- a/cirq-ionq/cirq_ionq/json_test_data/MSGate.json
+++ b/cirq-ionq/cirq_ionq/json_test_data/MSGate.json
@@ -1,5 +1,5 @@
 {
   "cirq_type": "MSGate",
-  "phi1": 0.1, 
-  "phi2": 0.55
+  "phi0": 0.1, 
+  "phi1": 0.55
 }
diff --git a/cirq-ionq/cirq_ionq/json_test_data/MSGate.repr b/cirq-ionq/cirq_ionq/json_test_data/MSGate.repr
index 1e1116467e1..61e1ed5152a 100644
--- a/cirq-ionq/cirq_ionq/json_test_data/MSGate.repr
+++ b/cirq-ionq/cirq_ionq/json_test_data/MSGate.repr
@@ -1 +1 @@
-cirq_ionq.MSGate(phi1=0.1, phi2=0.55)
+cirq_ionq.MSGate(phi0=0.1, phi1=0.55)
diff --git a/cirq-ionq/cirq_ionq/serializer_test.py b/cirq-ionq/cirq_ionq/serializer_test.py
index 3ddca1146b3..826fca96011 100644
--- a/cirq-ionq/cirq_ionq/serializer_test.py
+++ b/cirq-ionq/cirq_ionq/serializer_test.py
@@ -258,7 +258,7 @@ def test_serialize_native_gates():
     q0, q1, q2 = cirq.LineQubit.range(3)
     gpi = GPIGate(phi=0.1).on(q0)
     gpi2 = GPI2Gate(phi=0.2).on(q1)
-    ms = MSGate(phi1=0.3, phi2=0.4).on(q1, q2)
+    ms = MSGate(phi0=0.3, phi1=0.4).on(q1, q2)
     circuit = cirq.Circuit([gpi, gpi2, ms])
     serializer = ionq.Serializer()
     result = serializer.serialize(circuit)