diff --git a/src/braket/circuits/gates.py b/src/braket/circuits/gates.py
index dbc2e1a0b..9a4214c37 100644
--- a/src/braket/circuits/gates.py
+++ b/src/braket/circuits/gates.py
@@ -60,7 +60,14 @@
 
 
 class H(Gate):
-    """Hadamard gate."""
+    r"""Hadamard gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{H} = \frac{1}{\sqrt{2}} \begin{bmatrix}
+                1 & 1 \\
+                1 & -1 \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["H"])
@@ -91,7 +98,13 @@ def h(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Hadamard gate.
+
+        Unitary matrix:
+
+            .. math:: \mathtt{H} = \frac{1}{\sqrt{2}} \begin{bmatrix}
+                    1 & 1 \\
+                    1 & -1 \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -125,7 +138,14 @@ def h(
 
 
 class I(Gate):  # noqa: E742, E261
-    """Identity gate."""
+    r"""Identity gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{I} = \begin{bmatrix}
+                1 & 0 \\
+                0 & 1 \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["I"])
@@ -156,7 +176,13 @@ def i(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Identity gate.
+
+        Unitary matrix:
+
+            .. math:: \mathtt{I} = \begin{bmatrix}
+                    1 & 0 \\
+                    0 & 1 \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -190,7 +216,15 @@ def i(
 
 
 class X(Gate):
-    """Pauli-X gate."""
+    r"""Pauli-X gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{X} = \begin{bmatrix}
+                0 & 1 \\
+                1 & 0
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["X"])
@@ -221,7 +255,14 @@ def x(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Pauli-X gate.
+
+        Unitary matrix:
+
+            .. math:: \mathtt{X} = \begin{bmatrix}
+                    0 & 1 \\
+                    1 & 0
+                    \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -255,7 +296,15 @@ def x(
 
 
 class Y(Gate):
-    """Pauli-Y gate."""
+    r"""Pauli-Y gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{Y} = \begin{bmatrix}
+                0 & -i \\
+                i & 0
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["Y"])
@@ -286,7 +335,14 @@ def y(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Pauli-Y gate.
+
+        Unitary matrix:
+
+            .. math:: \mathtt{Y} = \begin{bmatrix}
+                    0 & -i \\
+                    i & 0
+                    \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -320,7 +376,15 @@ def y(
 
 
 class Z(Gate):
-    """Pauli-Z gate."""
+    r"""Pauli-Z gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{Z} = \begin{bmatrix}
+                1 & 0 \\
+                0 & -1
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["Z"])
@@ -351,7 +415,12 @@ def z(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Pauli-Z gate.
+
+        .. math:: \mathtt{Z} = \begin{bmatrix}
+                1 & 0 \\
+                0 & -1
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -385,7 +454,15 @@ def z(
 
 
 class S(Gate):
-    """S gate."""
+    r"""S gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{S} = \begin{bmatrix}
+                1 & 0 \\
+                0 & i
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["S"])
@@ -416,7 +493,12 @@ def s(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""S gate.
+
+        .. math:: \mathtt{S} = \begin{bmatrix}
+                1 & 0 \\
+                0 & i
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -450,7 +532,15 @@ def s(
 
 
 class Si(Gate):
-    """Conjugate transpose of S gate."""
+    r"""Conjugate transpose of S gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{S}^\dagger = \begin{bmatrix}
+                1 & 0 \\
+                0 & -i
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["Si"])
@@ -481,7 +571,12 @@ def si(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Conjugate transpose of S gate.
+
+        .. math:: \mathtt{S}^\dagger = \begin{bmatrix}
+                1 & 0 \\
+                0 & -i
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -515,7 +610,15 @@ def si(
 
 
 class T(Gate):
-    """T gate."""
+    r"""T gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{T} = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{i \pi/4}
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["T"])
@@ -546,7 +649,12 @@ def t(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""T gate.
+
+        .. math:: \mathtt{T} = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{i \pi/4}
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -580,7 +688,15 @@ def t(
 
 
 class Ti(Gate):
-    """Conjugate transpose of T gate."""
+    r"""Conjugate transpose of T gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{T}^\dagger = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{-i \pi/4}
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["Ti"])
@@ -611,7 +727,12 @@ def ti(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Conjugate transpose of T gate.
+
+        .. math:: \mathtt{T}^\dagger = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{-i \pi/4}
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -645,7 +766,15 @@ def ti(
 
 
 class V(Gate):
-    """Square root of not gate."""
+    r"""Square root of X gate (V gate).
+
+    Unitary matrix:
+
+        .. math:: \mathtt{V} = \frac{1}{2}\begin{bmatrix}
+                1+i & 1-i \\
+                1-i & 1+i
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["V"])
@@ -676,7 +805,12 @@ def v(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Square root of X gate (V gate).
+
+        .. math:: \mathtt{V} = \frac{1}{2}\begin{bmatrix}
+                1+i & 1-i \\
+                1-i & 1+i
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -710,7 +844,15 @@ def v(
 
 
 class Vi(Gate):
-    """Conjugate transpose of square root of not gate."""
+    r"""Conjugate transpose of square root of X gate (conjugate transpose of V).
+
+    Unitary matrix:
+
+        .. math:: \mathtt{V}^\dagger = \frac{1}{2}\begin{bmatrix}
+                1-i & 1+i \\
+                1+i & 1-i
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["Vi"])
@@ -741,7 +883,12 @@ def vi(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Conjugate transpose of square root of X gate (conjugate transpose of V).
+
+        .. math:: \mathtt{V}^\dagger = \frac{1}{2}\begin{bmatrix}
+                1-i & 1+i \\
+                1+i & 1-i
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s)
@@ -778,7 +925,14 @@ def vi(
 
 
 class Rx(AngledGate):
-    """X-axis rotation gate.
+    r"""X-axis rotation gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{R_x}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & -i \sin{(\phi/2)} \\
+                -i \sin{(\phi/2)} & \cos{(\phi/2)}
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -799,7 +953,7 @@ def _to_jaqcd(self, target: QubitSet, **kwargs) -> Any:
         return ir.Rx.construct(target=target[0], angle=self.angle)
 
     def to_matrix(self) -> np.ndarray:
-        """Returns a matrix representation of this gate.
+        r"""Returns a matrix representation of this gate.
         Returns:
             ndarray: The matrix representation of this gate.
         """
@@ -824,7 +978,12 @@ def rx(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""X-axis rotation gate.
+
+        .. math:: \mathtt{R_x}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & -i \sin{(\phi/2)} \\
+                -i \sin{(\phi/2)} & \cos{(\phi/2)}
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -858,7 +1017,14 @@ def rx(
 
 
 class Ry(AngledGate):
-    """Y-axis rotation gate.
+    r"""Y-axis rotation gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{R_y}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & -\sin{(\phi/2)} \\
+                \sin{(\phi/2)} & \cos{(\phi/2)}
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -879,7 +1045,7 @@ def _to_jaqcd(self, target: QubitSet) -> Any:
         return ir.Ry.construct(target=target[0], angle=self.angle)
 
     def to_matrix(self) -> np.ndarray:
-        """Returns a matrix representation of this gate.
+        r"""Returns a matrix representation of this gate.
         Returns:
             ndarray: The matrix representation of this gate.
         """
@@ -904,7 +1070,12 @@ def ry(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Y-axis rotation gate.
+
+        .. math:: \mathtt{R_y}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & -\sin{(\phi/2)} \\
+                \sin{(\phi/2)} & \cos{(\phi/2)}
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -923,6 +1094,7 @@ def ry(
         Returns:
             Iterable[Instruction]: Rx instruction.
 
+
         Examples:
             >>> circ = Circuit().ry(0, 0.15)
         """
@@ -938,7 +1110,14 @@ def ry(
 
 
 class Rz(AngledGate):
-    """Z-axis rotation gate.
+    r"""Z-axis rotation gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{R_z}(\phi) = \begin{bmatrix}
+                e^{-i \phi/2} & 0 \\
+                0 & e^{i \phi/2}
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -980,7 +1159,12 @@ def rz(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Z-axis rotation gate.
+
+        .. math:: \mathtt{R_z}(\phi) = \begin{bmatrix}
+                e^{-i \phi/2} & 0 \\
+                0 & e^{i \phi/2}
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -1014,7 +1198,14 @@ def rz(
 
 
 class PhaseShift(AngledGate):
-    """Phase shift gate.
+    r"""Phase shift gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{PhaseShift}(\phi) = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{i \phi}
+                \end{bmatrix}
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1054,7 +1245,12 @@ def phaseshift(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""Phase shift gate.
+
+        .. math:: \mathtt{PhaseShift}(\phi) = \begin{bmatrix}
+                1 & 0 \\
+                0 & e^{i \phi}
+                \end{bmatrix}
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -1095,7 +1291,17 @@ def phaseshift(
 
 
 class CNot(Gate):
-    """Controlled NOT gate."""
+    r"""Controlled NOT gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CNOT} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                0 & 0 & 1 & 0 \\
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "X"])
@@ -1128,7 +1334,14 @@ def fixed_qubit_count() -> int:
     @staticmethod
     @circuit.subroutine(register=True)
     def cnot(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled NOT gate.
+
+        .. math:: \mathtt{CNOT} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                0 & 0 & 1 & 0 \\
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1155,7 +1368,17 @@ def cnot(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instru
 
 
 class Swap(Gate):
-    """Swap gate."""
+    r"""Swap gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{SWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["SWAP", "SWAP"])
@@ -1195,7 +1418,14 @@ def swap(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Swap gate.
+
+        .. math:: \mathtt{SWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -1230,7 +1460,17 @@ def swap(
 
 
 class ISwap(Gate):
-    """ISwap gate."""
+    r"""ISwap gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{iSWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & i & 0 \\
+                0 & i & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["ISWAP", "ISWAP"])
@@ -1270,7 +1510,14 @@ def iswap(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""ISwap gate.
+
+        .. math:: \mathtt{iSWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & i & 0 \\
+                0 & i & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -1305,7 +1552,16 @@ def iswap(
 
 
 class PSwap(AngledGate):
-    """PSwap gate.
+    r"""PSwap gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{PSWAP}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & e^{i \phi} & 0 \\
+                0 & e^{i \phi} & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1357,7 +1613,14 @@ def pswap(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""PSwap gate.
+
+        .. math:: \mathtt{PSWAP}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 0 & e^{i \phi} & 0 \\
+                0 & e^{i \phi} & 0 & 0 \\
+                0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -1393,10 +1656,20 @@ def pswap(
 
 
 class XY(AngledGate):
-    """XY gate.
+    r"""XY gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{XY}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & \cos{(\phi/2)} & i\sin{(\phi/2)} & 0 \\
+                0 & i\sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                0 & 0 & 0 & 1 \\
+            \end{bmatrix}.
 
     Reference: https://arxiv.org/abs/1912.04424v1
 
+
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
     """
@@ -1419,7 +1692,7 @@ def _to_jaqcd(self, target: QubitSet) -> Any:
         return ir.XY.construct(targets=[target[0], target[1]], angle=self.angle)
 
     def to_matrix(self) -> np.ndarray:
-        """Returns a matrix representation of this gate.
+        r"""Returns a matrix representation of this gate.
         Returns:
             ndarray: The matrix representation of this gate.
         """
@@ -1453,7 +1726,14 @@ def xy(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""XY gate.
+
+        .. math:: \mathtt{XY}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & \cos{(\phi/2)} & i\sin{(\phi/2)} & 0 \\
+                0 & i\sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                0 & 0 & 0 & 1 \\
+            \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -1489,7 +1769,16 @@ def xy(
 
 
 class CPhaseShift(AngledGate):
-    """Controlled phase shift gate.
+    r"""Controlled phase shift gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CPhaseShift}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & e^{i \phi}
+            \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1527,7 +1816,14 @@ def cphaseshift(
         angle: Union[FreeParameterExpression, float],
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled phase shift gate.
+
+        .. math:: \mathtt{CPhaseShift}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & e^{i \phi}
+            \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1558,7 +1854,16 @@ def cphaseshift(
 
 
 class CPhaseShift00(AngledGate):
-    """Controlled phase shift gate for phasing the \\|00> state.
+    r"""Controlled phase shift gate for phasing the \|00> state.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CPhaseShift00}(\phi) = \begin{bmatrix}
+                e^{i \phi} & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 1
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1596,7 +1901,14 @@ def cphaseshift00(
         angle: Union[FreeParameterExpression, float],
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled phase shift gate for phasing the \|00> state.
+
+        .. math:: \mathtt{CPhaseShift00}(\phi) = \begin{bmatrix}
+                e^{i \phi} & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 1
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1627,7 +1939,16 @@ def cphaseshift00(
 
 
 class CPhaseShift01(AngledGate):
-    """Controlled phase shift gate for phasing the \\|01> state.
+    r"""Controlled phase shift gate for phasing the \|01> state.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CPhaseShift01}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & e^{i \phi} & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 1
+            \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1665,7 +1986,14 @@ def cphaseshift01(
         angle: Union[FreeParameterExpression, float],
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled phase shift gate for phasing the \|01> state.
+
+        .. math:: \mathtt{CPhaseShift01}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & e^{i \phi} & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 1
+            \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1696,7 +2024,16 @@ def cphaseshift01(
 
 
 class CPhaseShift10(AngledGate):
-    """Controlled phase shift gate for phasing the \\|10> state.
+    r"""Controlled phase shift gate for phasing the \\|10> state.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CPhaseShift10}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & e^{i \phi} & 0 \\
+                0 & 0 & 0 & 1
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -1734,7 +2071,14 @@ def cphaseshift10(
         angle: Union[FreeParameterExpression, float],
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled phase shift gate for phasing the \\|10> state.
+
+        .. math:: \mathtt{CPhaseShift10}(\phi) = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & e^{i \phi} & 0 \\
+                0 & 0 & 0 & 1
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1765,7 +2109,17 @@ def cphaseshift10(
 
 
 class CV(Gate):
-    """Controlled Sqrt of NOT gate."""
+    r"""Controlled Sqrt of X gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CV} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0.5+0.5i & 0.5-0.5i \\
+                0 & 0 & 0.5-0.5i & 0.5+0.5i
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "V"])
@@ -1798,7 +2152,14 @@ def fixed_qubit_count() -> int:
     @staticmethod
     @circuit.subroutine(register=True)
     def cv(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled Sqrt of X gate.
+
+        .. math:: \mathtt{CV} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0.5+0.5i & 0.5-0.5i \\
+                0 & 0 & 0.5-0.5i & 0.5+0.5i
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1825,7 +2186,17 @@ def cv(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruct
 
 
 class CY(Gate):
-    """Controlled Pauli-Y gate."""
+    r"""Controlled Pauli-Y gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CY} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & -i \\
+                0 & 0 & i & 0
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "Y"])
@@ -1858,7 +2229,14 @@ def fixed_qubit_count() -> int:
     @staticmethod
     @circuit.subroutine(register=True)
     def cy(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled Pauli-Y gate.
+
+        .. math:: \mathtt{CY} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & -i \\
+                0 & 0 & i & 0
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1885,7 +2263,17 @@ def cy(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruct
 
 
 class CZ(Gate):
-    """Controlled Pauli-Z gate."""
+    r"""Controlled Pauli-Z gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CZ} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & -1
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "Z"])
@@ -1910,7 +2298,14 @@ def fixed_qubit_count() -> int:
     @staticmethod
     @circuit.subroutine(register=True)
     def cz(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled Pauli-Z gate.
+
+        .. math:: \mathtt{CZ} = \begin{bmatrix}
+                1 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 \\
+                0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & -1
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -1937,7 +2332,17 @@ def cz(control: QubitSetInput, target: QubitInput, power: float = 1) -> Instruct
 
 
 class ECR(Gate):
-    """An echoed RZX(pi/2) gate."""
+    r"""An echoed RZX(pi/2) gate (ECR gate).
+
+    Unitary matrix:
+
+        .. math:: \mathtt{ECR} = \begin{bmatrix}
+                0 & 0 & 1 & i \\
+                0 & 0 & i & 1 \\
+                1 & -i & 0 & 0 \\
+                -i & 1 & 0 & 0
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["ECR", "ECR"])
@@ -1976,7 +2381,14 @@ def ecr(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""An echoed RZX(pi/2) gate (ECR gate).
+
+        .. math:: \mathtt{ECR} = \begin{bmatrix}
+                0 & 0 & 1 & i \\
+                0 & 0 & i & 1 \\
+                1 & -i & 0 & 0 \\
+                -i & 1 & 0 & 0
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -2011,7 +2423,16 @@ def ecr(
 
 
 class XX(AngledGate):
-    """Ising XX coupling gate.
+    r"""Ising XX coupling gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{XX}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & 0 & 0 & -i \sin{(\phi/2)} \\
+                0 & \cos{(\phi/2)} & -i \sin{(\phi/2)} & 0 \\
+                0 & -i \sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                -i \sin{(\phi/2)} & 0 & 0 & \cos{(\phi/2)}
+                \end{bmatrix}.
 
     Reference: https://arxiv.org/abs/1707.06356
 
@@ -2037,7 +2458,7 @@ def _to_jaqcd(self, target: QubitSet) -> Any:
         return ir.XX.construct(targets=[target[0], target[1]], angle=self.angle)
 
     def to_matrix(self) -> np.ndarray:
-        """Returns a matrix representation of this gate.
+        r"""Returns a matrix representation of this gate.
         Returns:
             ndarray: The matrix representation of this gate.
         """
@@ -2071,7 +2492,14 @@ def xx(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Ising XX coupling gate.
+
+        .. math:: \mathtt{XX}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & 0 & 0 & -i \sin{(\phi/2)} \\
+                0 & \cos{(\phi/2)} & -i \sin{(\phi/2)} & 0 \\
+                0 & -i \sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                -i \sin{(\phi/2)} & 0 & 0 & \cos{(\phi/2)}
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -2107,7 +2535,16 @@ def xx(
 
 
 class YY(AngledGate):
-    """Ising YY coupling gate.
+    r"""Ising YY coupling gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{YY}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & 0 & 0 & i \sin{(\phi/2)} \\
+                0 & \cos{(\phi/2)} & -i \sin{(\phi/2)} & 0 \\
+                0 & -i \sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                i \sin{(\phi/2)} & 0 & 0 & \cos{(\phi/2)}
+                \end{bmatrix}.
 
     Reference: https://arxiv.org/abs/1707.06356
 
@@ -2133,7 +2570,7 @@ def _to_jaqcd(self, target: QubitSet) -> Any:
         return ir.YY.construct(targets=[target[0], target[1]], angle=self.angle)
 
     def to_matrix(self) -> np.ndarray:
-        """Returns a matrix representation of this gate.
+        r"""Returns a matrix representation of this gate.
         Returns:
             ndarray: The matrix representation of this gate.
         """
@@ -2167,7 +2604,14 @@ def yy(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Ising YY coupling gate.
+
+        .. math:: \mathtt{YY}(\phi) = \begin{bmatrix}
+                \cos{(\phi/2)} & 0 & 0 & i \sin{(\phi/2)} \\
+                0 & \cos{(\phi/2)} & -i \sin{(\phi/2)} & 0 \\
+                0 & -i \sin{(\phi/2)} & \cos{(\phi/2)} & 0 \\
+                i \sin{(\phi/2)} & 0 & 0 & \cos{(\phi/2)}
+                \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -2203,7 +2647,16 @@ def yy(
 
 
 class ZZ(AngledGate):
-    """Ising ZZ coupling gate.
+    r"""Ising ZZ coupling gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{ZZ}(\phi) = \begin{bmatrix}
+                e^{-i\phi/2} & 0 & 0 & 0 \\
+                0 & e^{i\phi/2} & 0 & 0 \\
+                0 & 0 & e^{i\phi/2} & 0 \\
+                0 & 0 & 0 & e^{-i\phi/2}
+            \end{bmatrix}.
 
     Reference: https://arxiv.org/abs/1707.06356
 
@@ -2257,7 +2710,14 @@ def zz(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Ising ZZ coupling gate.
+
+        .. math:: \mathtt{ZZ}(\phi) = \begin{bmatrix}
+                e^{-i\phi/2} & 0 & 0 & 0 \\
+                0 & e^{i\phi/2} & 0 & 0 \\
+                0 & 0 & e^{i\phi/2} & 0 \\
+                0 & 0 & 0 & e^{-i\phi/2}
+            \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -2296,7 +2756,21 @@ def zz(
 
 
 class CCNot(Gate):
-    """CCNOT gate or Toffoli gate."""
+    r"""CCNOT gate or Toffoli gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CCNOT} = \begin{bmatrix}
+                1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\
+                0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "C", "X"])
@@ -2341,7 +2815,18 @@ def ccnot(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""CCNOT gate or Toffoli gate.
+
+        .. math:: \mathtt{CCNOT} = \begin{bmatrix}
+                1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\
+                0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+                \end{bmatrix}.
 
         Args:
             control1 (QubitInput): Control qubit 1 index.
@@ -2379,7 +2864,21 @@ def ccnot(
 
 
 class CSwap(Gate):
-    """Controlled Swap gate."""
+    r"""Controlled Swap gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{CSWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\
+                0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
+    """
 
     def __init__(self):
         super().__init__(qubit_count=None, ascii_symbols=["C", "SWAP", "SWAP"])
@@ -2421,7 +2920,18 @@ def cswap(
         target2: QubitInput,
         power: float = 1,
     ) -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Controlled Swap gate.
+
+        .. math:: \mathtt{CSWAP} = \begin{bmatrix}
+                1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 1 & 0 & 0 & 0 & 0 & 0 & 0  \\
+                0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\
+                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\
+                \end{bmatrix}.
 
         Args:
             control (QubitSetInput): Control qubit(s). The last control qubit
@@ -2452,7 +2962,14 @@ def cswap(
 
 
 class GPi(AngledGate):
-    """IonQ GPi gate.
+    r"""IonQ GPi gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{GPi}(\phi) = \begin{bmatrix}
+                0 & e^{-i \phi} \\
+                e^{i \phi} & 0
+                \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -2497,7 +3014,12 @@ def gpi(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""IonQ GPi gate.
+
+        .. math:: \mathtt{GPi}(\phi) = \begin{bmatrix}
+                0 & e^{-i \phi} \\
+                e^{i \phi} & 0
+                \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -2531,7 +3053,14 @@ def gpi(
 
 
 class GPi2(AngledGate):
-    """IonQ GPi2 gate.
+    r"""IonQ GPi2 gate.
+
+    Unitary matrix:
+
+        .. math:: \mathtt{GPi2}(\phi) = \begin{bmatrix}
+                1 & -i e^{-i \phi} \\
+                -i e^{i \phi} & 1
+            \end{bmatrix}.
 
     Args:
         angle (Union[FreeParameterExpression, float]): angle in radians.
@@ -2576,7 +3105,12 @@ def gpi2(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""IonQ GPi2 gate.
+
+        .. math:: \mathtt{GPi2}(\phi) = \begin{bmatrix}
+                1 & -i e^{-i \phi} \\
+                -i e^{i \phi} & 1
+            \end{bmatrix}.
 
         Args:
             target (QubitSetInput): Target qubit(s).
@@ -2610,12 +3144,26 @@ def gpi2(
 
 
 class MS(TripleAngledGate):
-    """IonQ Mølmer-Sørenson gate.
+    r"""IonQ Mølmer-Sørensen gate.
+
+    Unitary matrix:
+
+            .. math:: &\mathtt{MS}(\phi_0, \phi_1, \theta) =\\ &\begin{bmatrix}
+                    \cos{\frac{\theta}{2}} & 0 &
+                    0 & -ie^{-i (\phi_0 + \phi_1)}\sin{\frac{\theta}{2}} \\
+                    0 & \cos{\frac{\theta}{2}} &
+                    -ie^{-i (\phi_0 - \phi_1)}\sin{\frac{\theta}{2}} & 0 \\
+                    0 & -ie^{i (\phi_0 - \phi_1)}\sin{\frac{\theta}{2}} &
+                    \cos{\frac{\theta}{2}} & 0 \\
+                    -ie^{i (\phi_0 + \phi_1)}\sin{\frac{\theta}{2}} & 0
+                    & 0 & \cos{\frac{\theta}{2}}
+                    \end{bmatrix}.
 
     Args:
         angle_1 (Union[FreeParameterExpression, float]): angle in radians.
         angle_2 (Union[FreeParameterExpression, float]): angle in radians.
         angle_3 (Union[FreeParameterExpression, float]): angle in radians.
+        Default value is angle_3=pi/2.
     """
 
     def __init__(
@@ -2689,7 +3237,18 @@ def ms(
         control_state: Optional[BasisStateInput] = None,
         power: float = 1,
     ) -> Iterable[Instruction]:
-        """Registers this function into the circuit class.
+        r"""IonQ Mølmer-Sørensen gate.
+
+        .. math:: &\mathtt{MS}(\phi_0, \phi_1, \theta) =\\ &\begin{bmatrix}
+                    \cos{\frac{\theta}{2}} & 0 &
+                    0 & -ie^{-i (\phi_0 + \phi_1)}\sin{\frac{\theta}{2}} \\
+                    0 & \cos{\frac{\theta}{2}} &
+                    -ie^{-i (\phi_0 - \phi_1)}\sin{\frac{\theta}{2}} & 0 \\
+                    0 & -ie^{i (\phi_0 - \phi_1)}\sin{\frac{\theta}{2}} &
+                    \cos{\frac{\theta}{2}} & 0 \\
+                    -ie^{i (\phi_0 + \phi_1)}\sin{\frac{\theta}{2}} & 0
+                    & 0 & \cos{\frac{\theta}{2}}
+                    \end{bmatrix}.
 
         Args:
             target1 (QubitInput): Target qubit 1 index.
@@ -2729,7 +3288,7 @@ def ms(
 
 
 class Unitary(Gate):
-    """Arbitrary unitary gate
+    """Arbitrary unitary gate.
 
     Args:
         matrix (numpy.ndarray): Unitary matrix which defines the gate.
@@ -2792,7 +3351,7 @@ def _transform_matrix_to_ir(matrix: np.ndarray) -> list:
     @staticmethod
     @circuit.subroutine(register=True)
     def unitary(targets: QubitSet, matrix: np.ndarray, display_name: str = "U") -> Instruction:
-        """Registers this function into the circuit class.
+        r"""Arbitrary unitary gate.
 
         Args:
             targets (QubitSet): Target qubits.
@@ -2849,7 +3408,7 @@ def pulse_sequence(self) -> PulseSequence:
 
     @property
     def parameters(self) -> list[FreeParameter]:
-        """Returns the list of `FreeParameter` s associated with the gate."""
+        r"""Returns the list of `FreeParameter` s associated with the gate."""
         return list(self._pulse_sequence.parameters)
 
     def bind_values(self, **kwargs) -> PulseGate: