diff --git a/qiskit/circuit/library/__init__.py b/qiskit/circuit/library/__init__.py
index 73588a421ac7..4a763856c82d 100644
--- a/qiskit/circuit/library/__init__.py
+++ b/qiskit/circuit/library/__init__.py
@@ -211,9 +211,15 @@
    :template: autosummary/class_no_inherited_members.rst
 
    AND
+   AndGate
    OR
+   OrGate
    XOR
+   BitwiseXorGate
    InnerProduct
+   InnerProductGate
+
+.. autofunction:: random_bitwise_xor
 
 Basis Change Circuits
 =====================
@@ -523,9 +529,14 @@
 from .hamiltonian_gate import HamiltonianGate
 from .boolean_logic import (
     AND,
+    AndGate,
     OR,
+    OrGate,
     XOR,
+    BitwiseXorGate,
+    random_bitwise_xor,
     InnerProduct,
+    InnerProductGate,
 )
 from .basis_change import QFT, QFTGate
 from .arithmetic import (
diff --git a/qiskit/circuit/library/boolean_logic/__init__.py b/qiskit/circuit/library/boolean_logic/__init__.py
index b273f0d6a245..736f983b05f9 100644
--- a/qiskit/circuit/library/boolean_logic/__init__.py
+++ b/qiskit/circuit/library/boolean_logic/__init__.py
@@ -12,7 +12,7 @@
 
 """The Boolean logic circuit library."""
 
-from .quantum_and import AND
-from .quantum_or import OR
-from .quantum_xor import XOR
-from .inner_product import InnerProduct
+from .quantum_and import AND, AndGate
+from .quantum_or import OR, OrGate
+from .quantum_xor import XOR, BitwiseXorGate, random_bitwise_xor
+from .inner_product import InnerProduct, InnerProductGate
diff --git a/qiskit/circuit/library/boolean_logic/inner_product.py b/qiskit/circuit/library/boolean_logic/inner_product.py
index dcaced069119..84b3807fb56c 100644
--- a/qiskit/circuit/library/boolean_logic/inner_product.py
+++ b/qiskit/circuit/library/boolean_logic/inner_product.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020.
+# (C) Copyright IBM 2020, 2024.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -11,10 +11,11 @@
 # that they have been altered from the originals.
 
 
-"""InnerProduct circuit."""
+"""InnerProduct circuit and gate."""
 
 
-from qiskit.circuit import QuantumRegister, QuantumCircuit
+from qiskit.circuit import QuantumRegister, QuantumCircuit, Gate
+from qiskit.utils.deprecation import deprecate_func
 
 
 class InnerProduct(QuantumCircuit):
@@ -61,6 +62,11 @@ class InnerProduct(QuantumCircuit):
            _generate_circuit_library_visualization(circuit)
     """
 
+    @deprecate_func(
+        since="1.3",
+        additional_msg="Use qiskit.circuit.library.InnerProductGate instead.",
+        pending=True,
+    )
     def __init__(self, num_qubits: int) -> None:
         """Return a circuit to compute the inner product of 2 n-qubit registers.
 
@@ -76,3 +82,74 @@ def __init__(self, num_qubits: int) -> None:
 
         super().__init__(*inner.qregs, name="inner_product")
         self.compose(inner.to_gate(), qubits=self.qubits, inplace=True)
+
+
+class InnerProductGate(Gate):
+    r"""A 2n-qubit Boolean function that computes the inner product of
+    two n-qubit vectors over :math:`F_2`.
+
+    This implementation is a phase oracle which computes the following transform.
+
+    .. math::
+
+        \mathcal{IP}_{2n} : F_2^{2n} \rightarrow {-1, 1}
+        \mathcal{IP}_{2n}(x_1, \cdots, x_n, y_1, \cdots, y_n) = (-1)^{x.y}
+
+    The corresponding unitary is a diagonal, which induces a -1 phase on any inputs
+    where the inner product of the top and bottom registers is 1. Otherwise, it keeps
+    the input intact.
+
+    .. parsed-literal::
+
+
+        q0_0: ─■──────────
+               │
+        q0_1: ─┼──■───────
+               │  │
+        q0_2: ─┼──┼──■────
+               │  │  │
+        q0_3: ─┼──┼──┼──■─
+               │  │  │  │
+        q1_0: ─■──┼──┼──┼─
+                  │  │  │
+        q1_1: ────■──┼──┼─
+                     │  │
+        q1_2: ───────■──┼─
+                        │
+        q1_3: ──────────■─
+
+
+    Reference Circuit:
+        .. plot::
+
+           from qiskit.circuit import QuantumCircuit
+           from qiskit.circuit.library import InnerProductGate
+           from qiskit.visualization.library import _generate_circuit_library_visualization
+           circuit = QuantumCircuit(8)
+           circuit.append(InnerProductGate(4), [0, 1, 2, 3, 4, 5, 6, 7])
+           _generate_circuit_library_visualization(circuit)
+    """
+
+    def __init__(
+        self,
+        num_qubits: int,
+    ) -> None:
+        """
+        Args:
+            num_qubits: width of top and bottom registers (half total number of qubits).
+        """
+        super().__init__("inner_product", 2 * num_qubits, [])
+
+    def _define(self):
+        num_qubits = self.num_qubits // 2
+        qr_a = QuantumRegister(num_qubits, name="x")
+        qr_b = QuantumRegister(num_qubits, name="y")
+
+        circuit = QuantumCircuit(qr_a, qr_b, name="inner_product")
+        for i in range(num_qubits):
+            circuit.cz(qr_a[i], qr_b[i])
+
+        self.definition = circuit
+
+    def __eq__(self, other):
+        return isinstance(other, InnerProductGate) and self.num_qubits == other.num_qubits
diff --git a/qiskit/circuit/library/boolean_logic/quantum_and.py b/qiskit/circuit/library/boolean_logic/quantum_and.py
index ce2d253ca85a..53099aa7be84 100644
--- a/qiskit/circuit/library/boolean_logic/quantum_and.py
+++ b/qiskit/circuit/library/boolean_logic/quantum_and.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020.
+# (C) Copyright IBM 2020, 2024.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -11,11 +11,13 @@
 # that they have been altered from the originals.
 
 
-"""Implementations of boolean logic quantum circuits."""
+"""Boolean AND circuit and gate."""
+
 from __future__ import annotations
 
-from qiskit.circuit import QuantumRegister, QuantumCircuit, AncillaRegister
+from qiskit.circuit import QuantumRegister, QuantumCircuit, AncillaRegister, Gate
 from qiskit.circuit.library.standard_gates import MCXGate
+from qiskit.utils.deprecation import deprecate_func
 
 
 class AND(QuantumCircuit):
@@ -49,6 +51,11 @@ class AND(QuantumCircuit):
 
     """
 
+    @deprecate_func(
+        since="1.3",
+        additional_msg="Use qiskit.circuit.library.AndGate instead.",
+        pending=True,
+    )
     def __init__(
         self,
         num_variable_qubits: int,
@@ -58,7 +65,7 @@ def __init__(
         """Create a new logical AND circuit.
 
         Args:
-            num_variable_qubits: The qubits of which the OR is computed. The result will be written
+            num_variable_qubits: The qubits of which the AND is computed. The result will be written
                 into an additional result qubit.
             flags: A list of +1/0/-1 marking negations or omissions of qubits.
             mcx_mode: The mode to be used to implement the multi-controlled X gate.
@@ -95,3 +102,99 @@ def __init__(
 
         super().__init__(*circuit.qregs, name="and")
         self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)
+
+
+class AndGate(Gate):
+    r"""A gate representing the logical AND operation on a number of qubits.
+
+    For the AND operation the state :math:`|1\rangle` is interpreted as ``True``. The result
+    qubit is flipped, if the state of all variable qubits is ``True``. In this format, the AND
+    operation equals a multi-controlled X gate, which is controlled on all variable qubits.
+    Using a list of flags however, qubits can be skipped or negated. Practically, the flags
+    allow to skip controls or to apply pre- and post-X gates to the negated qubits.
+
+    The AndGate gate without special flags equals the multi-controlled-X gate:
+
+    .. plot::
+
+       from qiskit.circuit import QuantumCircuit
+       from qiskit.circuit.library import AndGate
+       from qiskit.visualization.library import _generate_circuit_library_visualization
+       circuit = QuantumCircuit(6)
+       circuit.append(AndGate(5), [0, 1, 2, 3, 4, 5])
+       _generate_circuit_library_visualization(circuit)
+
+    Using flags we can negate qubits or skip them. For instance, if we have 5 qubits and want to
+    return ``True`` if the first qubit is ``False`` and the last two are ``True`` we use the flags
+    ``[-1, 0, 0, 1, 1]``.
+
+    .. plot::
+
+       from qiskit.circuit import QuantumCircuit
+       from qiskit.circuit.library import AndGate
+       from qiskit.visualization.library import _generate_circuit_library_visualization
+       circuit = QuantumCircuit(6)
+       circuit.append(AndGate(5, flags=[-1, 0, 0, 1, 1]), [0, 1, 2, 3, 4, 5])
+       _generate_circuit_library_visualization(circuit)
+
+    """
+
+    def __init__(
+        self,
+        num_variable_qubits: int,
+        flags: list[int] | None = None,
+    ) -> None:
+        """
+        Args:
+            num_variable_qubits: The qubits of which the AND is computed. The result will be written
+                into an additional result qubit.
+            flags: A list of +1/0/-1 marking negations or omissions of qubits.
+        """
+        super().__init__("and", num_variable_qubits + 1, [])
+        self.num_variable_qubits = num_variable_qubits
+        self.flags = flags
+
+    def _define(self):
+        # add registers
+        qr_variable = QuantumRegister(self.num_variable_qubits, name="variable")
+        qr_result = QuantumRegister(1, name="result")
+
+        # determine the control qubits: all that have a nonzero flag
+        flags = self.flags or [1] * self.num_variable_qubits
+        control_qubits = [q for q, flag in zip(qr_variable, flags) if flag != 0]
+
+        # determine the qubits that need to be flipped (if a flag is < 0)
+        flip_qubits = [q for q, flag in zip(qr_variable, flags) if flag < 0]
+
+        # create the definition circuit
+        circuit = QuantumCircuit(qr_variable, qr_result, name="and")
+
+        if len(flip_qubits) > 0:
+            circuit.x(flip_qubits)
+        circuit.mcx(control_qubits, qr_result[:])
+        if len(flip_qubits) > 0:
+            circuit.x(flip_qubits)
+
+        self.definition = circuit
+
+    # pylint: disable=unused-argument
+    def inverse(self, annotated: bool = False):
+        r"""Return inverted AND gate (itself).
+
+        Args:
+            annotated: when set to ``True``, this is typically used to return an
+                :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete
+                :class:`.Gate`. However, for this class this argument is ignored as this gate
+                is self-inverse.
+
+        Returns:
+            AndGate: inverse gate (self-inverse).
+        """
+        return AndGate(self.num_variable_qubits, self.flags)
+
+    def __eq__(self, other):
+        return (
+            isinstance(other, AndGate)
+            and self.num_variable_qubits == other.num_variable_qubits
+            and self.flags == other.flags
+        )
diff --git a/qiskit/circuit/library/boolean_logic/quantum_or.py b/qiskit/circuit/library/boolean_logic/quantum_or.py
index 91d6c4fbdd52..95b346b34846 100644
--- a/qiskit/circuit/library/boolean_logic/quantum_or.py
+++ b/qiskit/circuit/library/boolean_logic/quantum_or.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020.
+# (C) Copyright IBM 2020, 2024.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -11,12 +11,14 @@
 # that they have been altered from the originals.
 
 
-"""Implementations of boolean logic quantum circuits."""
+"""Boolean OR circuit and gate."""
+
 from __future__ import annotations
 from typing import List, Optional
 
-from qiskit.circuit import QuantumRegister, QuantumCircuit, AncillaRegister
+from qiskit.circuit import QuantumRegister, QuantumCircuit, AncillaRegister, Gate
 from qiskit.circuit.library.standard_gates import MCXGate
+from qiskit.utils.deprecation import deprecate_func
 
 
 class OR(QuantumCircuit):
@@ -50,6 +52,11 @@ class OR(QuantumCircuit):
 
     """
 
+    @deprecate_func(
+        since="1.3",
+        additional_msg="Use qiskit.circuit.library.OrGate instead.",
+        pending=True,
+    )
     def __init__(
         self,
         num_variable_qubits: int,
@@ -96,3 +103,100 @@ def __init__(
 
         super().__init__(*circuit.qregs, name="or")
         self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)
+
+
+class OrGate(Gate):
+    r"""A gate representing the logical OR operation on a number of qubits.
+
+    For the OR operation the state :math:`|1\rangle` is interpreted as ``True``. The result
+    qubit is flipped, if the state of any variable qubit is ``True``. The OR is implemented using
+    a multi-open-controlled X gate (i.e. flips if the state is :math:`|0\rangle`) and
+    applying an X gate on the result qubit.
+    Using a list of flags, qubits can be skipped or negated.
+
+    The OrGate gate without special flags:
+
+    .. plot::
+
+       from qiskit.circuit import QuantumCircuit
+       from qiskit.circuit.library import OrGate
+       from qiskit.visualization.library import _generate_circuit_library_visualization
+       circuit = QuantumCircuit(6)
+       circuit.append(OrGate(5), [0, 1, 2, 3, 4, 5])
+       _generate_circuit_library_visualization(circuit)
+
+    Using flags we can negate qubits or skip them. For instance, if we have 5 qubits and want to
+    return ``True`` if the first qubit is ``False`` or one of the last two are ``True`` we use the
+    flags ``[-1, 0, 0, 1, 1]``.
+
+    .. plot::
+
+       from qiskit.circuit import QuantumCircuit
+       from qiskit.circuit.library import OrGate
+       from qiskit.visualization.library import _generate_circuit_library_visualization
+       circuit = QuantumCircuit(6)
+       circuit.append(OrGate(5, flags=[-1, 0, 0, 1, 1]), [0, 1, 2, 3, 4, 5])
+       _generate_circuit_library_visualization(circuit)
+
+    """
+
+    def __init__(
+        self,
+        num_variable_qubits: int,
+        flags: list[int] | None = None,
+    ) -> None:
+        """
+        Args:
+            num_variable_qubits: The qubits of which the AND is computed. The result will be written
+                into an additional result qubit.
+            flags: A list of +1/0/-1 marking negations or omissions of qubits.
+        """
+        super().__init__("and", num_variable_qubits + 1, [])
+        self.num_variable_qubits = num_variable_qubits
+        self.flags = flags
+
+    def _define(self):
+        # add registers
+        qr_variable = QuantumRegister(self.num_variable_qubits, name="variable")
+        qr_result = QuantumRegister(1, name="result")
+
+        # determine the control qubits: all that have a nonzero flag
+        flags = self.flags or [1] * self.num_variable_qubits
+        control_qubits = [q for q, flag in zip(qr_variable, flags) if flag != 0]
+
+        # determine the qubits that need to be flipped (if a flag is > 0)
+        flip_qubits = [q for q, flag in zip(qr_variable, flags) if flag > 0]
+
+        # create the definition circuit
+        circuit = QuantumCircuit(qr_variable, qr_result, name="or")
+
+        circuit.x(qr_result)
+        if len(flip_qubits) > 0:
+            circuit.x(flip_qubits)
+        circuit.mcx(control_qubits, qr_result[:])
+        if len(flip_qubits) > 0:
+            circuit.x(flip_qubits)
+
+        self.definition = circuit
+
+    # pylint: disable=unused-argument
+    def inverse(self, annotated: bool = False):
+        r"""Return inverted OR gate (itself).
+
+        Args:
+            annotated: when set to ``True``, this is typically used to return an
+                :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete
+                :class:`.Gate`. However, for this class this argument is ignored as this gate
+                is self-inverse.
+
+        Returns:
+            OrGate: inverse gate (self-inverse).
+        """
+        return OrGate(self.num_variable_qubits, self.flags)
+
+    def __eq__(self, other):
+        return (
+            isinstance(other, OrGate)
+            and self.num_variable_qubits == other.num_variable_qubits
+            and self.flags == other.flags
+        )
diff --git a/qiskit/circuit/library/boolean_logic/quantum_xor.py b/qiskit/circuit/library/boolean_logic/quantum_xor.py
index 5b230345137d..73a2178830bc 100644
--- a/qiskit/circuit/library/boolean_logic/quantum_xor.py
+++ b/qiskit/circuit/library/boolean_logic/quantum_xor.py
@@ -1,6 +1,6 @@
 # This code is part of Qiskit.
 #
-# (C) Copyright IBM 2020.
+# (C) Copyright IBM 2020, 2024.
 #
 # This code is licensed under the Apache License, Version 2.0. You may
 # obtain a copy of this license in the LICENSE.txt file in the root directory
@@ -11,13 +11,14 @@
 # that they have been altered from the originals.
 
 
-"""XOR circuit."""
+"""Bitwise XOR circuit and gate."""
 
 from typing import Optional
 
 import numpy as np
-from qiskit.circuit import QuantumCircuit
+from qiskit.circuit import QuantumCircuit, Gate
 from qiskit.circuit.exceptions import CircuitError
+from qiskit.utils.deprecation import deprecate_func
 
 
 class XOR(QuantumCircuit):
@@ -28,6 +29,12 @@ class XOR(QuantumCircuit):
     This circuit can also represent addition by ``amount`` over the finite field GF(2).
     """
 
+    @deprecate_func(
+        since="1.3",
+        additional_msg="Instead, for xor-ing with a specified amount, use BitwiseXorGate,"
+        "and for xor-ing with a random amount, use random_bitwise_xor.",
+        pending=True,
+    )
     def __init__(
         self,
         num_qubits: int,
@@ -69,3 +76,90 @@ def __init__(
 
         super().__init__(*circuit.qregs, name="xor")
         self.compose(circuit.to_gate(), qubits=self.qubits, inplace=True)
+
+
+class BitwiseXorGate(Gate):
+    """An n-qubit gate for bitwise xor-ing the input with some integer ``amount``.
+
+    The ``amount`` is xor-ed in bitstring form with the input.
+
+    This gate can also represent addition by ``amount`` over the finite field GF(2).
+
+    Reference Circuit:
+
+    .. plot::
+
+       from qiskit.circuit import QuantumCircuit
+       from qiskit.circuit.library import BitwiseXorGate
+       from qiskit.visualization.library import _generate_circuit_library_visualization
+       circuit = QuantumCircuit(5)
+       circuit.append(BitwiseXorGate(5, amount=12), [0, 1, 2, 3, 4])
+       _generate_circuit_library_visualization(circuit)
+
+    """
+
+    def __init__(
+        self,
+        num_qubits: int,
+        amount: int,
+    ) -> None:
+        """
+        Args:
+            num_qubits: the width of circuit.
+            amount: the xor amount in decimal form.
+
+        Raises:
+            CircuitError: if the xor bitstring exceeds available qubits.
+        """
+        if len(bin(amount)[2:]) > num_qubits:
+            raise CircuitError("Bits in 'amount' exceed circuit width")
+
+        super().__init__("xor", num_qubits, [])
+        self.amount = amount
+
+    def _define(self):
+        circuit = QuantumCircuit(self.num_qubits, name="xor")
+        amount = self.amount
+        for i in range(self.num_qubits):
+            bit = amount & 1
+            amount = amount >> 1
+            if bit == 1:
+                circuit.x(i)
+
+        self.definition = circuit
+
+    def __eq__(self, other):
+        return (
+            isinstance(other, BitwiseXorGate)
+            and self.num_qubits == other.num_qubits
+            and self.amount == other.amount
+        )
+
+    # pylint: disable=unused-argument
+    def inverse(self, annotated: bool = False):
+        r"""Return inverted BitwiseXorGate gate (itself).
+
+        Args:
+            annotated: when set to ``True``, this is typically used to return an
+                :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete
+                :class:`.Gate`. However, for this class this argument is ignored as this gate
+                is self-inverse.
+
+        Returns:
+            BitwiseXorGate: inverse gate (self-inverse).
+        """
+        return BitwiseXorGate(self.num_qubits, self.amount)
+
+
+def random_bitwise_xor(num_qubits: int, seed: int) -> BitwiseXorGate:
+    """
+    Create a random BitwiseXorGate.
+
+    Args:
+        num_qubits: the width of circuit.
+        seed: random seed in case a random xor is requested.
+    """
+
+    rng = np.random.default_rng(seed)
+    amount = rng.integers(0, 2**num_qubits)
+    return BitwiseXorGate(num_qubits, amount)
diff --git a/releasenotes/notes/boolean-logic-gates-40add5cf0b20b5e9.yaml b/releasenotes/notes/boolean-logic-gates-40add5cf0b20b5e9.yaml
new file mode 100644
index 000000000000..d1de403ab4f7
--- /dev/null
+++ b/releasenotes/notes/boolean-logic-gates-40add5cf0b20b5e9.yaml
@@ -0,0 +1,14 @@
+---
+features_circuits:
+  - |
+    Quantum circuits in :mod:`qiskit.circuit.library.boolean_logic` now have equivalent
+    representations as :class:`.Gate` objects:
+
+    * :class:`~qiskit.circuit.library.AndGate`,
+      representing :class:`~qiskit.circuit.library.AND`,
+    * :class:`~qiskit.circuit.library.OrGate`,
+      representing :class:`~qiskit.circuit.library.OR`,
+    * :class:`~qiskit.circuit.library.BitwiseXorGate`,
+      representing :class:`~qiskit.circuit.library.XOR`,
+    * :class:`~qiskit.circuit.library.InnerProductGate`,
+      representing :class:`~qiskit.circuit.library.InnerProduct`.
diff --git a/test/python/circuit/library/test_boolean_logic.py b/test/python/circuit/library/test_boolean_logic.py
index cdadc9142a97..265f494f4c0c 100644
--- a/test/python/circuit/library/test_boolean_logic.py
+++ b/test/python/circuit/library/test_boolean_logic.py
@@ -16,9 +16,18 @@
 from ddt import ddt, data, unpack
 import numpy as np
 
-from qiskit.circuit import QuantumCircuit
-from qiskit.circuit.library import XOR, InnerProduct, AND, OR
-from qiskit.quantum_info import Statevector
+from qiskit.circuit import QuantumCircuit, Gate
+from qiskit.circuit.library import (
+    XOR,
+    InnerProduct,
+    AND,
+    OR,
+    AndGate,
+    OrGate,
+    BitwiseXorGate,
+    InnerProductGate,
+)
+from qiskit.quantum_info import Statevector, Operator
 from test import QiskitTestCase  # pylint: disable=wrong-import-order
 
 
@@ -26,11 +35,15 @@
 class TestBooleanLogicLibrary(QiskitTestCase):
     """Test library of boolean logic quantum circuits."""
 
-    def assertBooleanFunctionIsCorrect(self, boolean_circuit, reference):
-        """Assert that ``boolean_circuit`` implements the reference boolean function correctly."""
-        circuit = QuantumCircuit(boolean_circuit.num_qubits)
-        circuit.h(list(range(boolean_circuit.num_variable_qubits)))
-        circuit.append(boolean_circuit.to_instruction(), list(range(boolean_circuit.num_qubits)))
+    def assertBooleanFunctionIsCorrect(self, boolean_object, reference):
+        """Assert that ``boolean_object`` implements the reference boolean function correctly."""
+        circuit = QuantumCircuit(boolean_object.num_qubits)
+        circuit.h(list(range(boolean_object.num_variable_qubits)))
+
+        if isinstance(boolean_object, Gate):
+            circuit.append(boolean_object, list(range(boolean_object.num_qubits)))
+        else:
+            circuit.append(boolean_object.to_instruction(), list(range(boolean_object.num_qubits)))
 
         # compute the statevector of the circuit
         statevector = Statevector.from_label("0" * circuit.num_qubits)
@@ -38,18 +51,18 @@ def assertBooleanFunctionIsCorrect(self, boolean_circuit, reference):
 
         # trace out ancillas
         probabilities = statevector.probabilities(
-            qargs=list(range(boolean_circuit.num_variable_qubits + 1))
+            qargs=list(range(boolean_object.num_variable_qubits + 1))
         )
 
         # compute the expected outcome by computing the entries of the statevector that should
         # have a 1 / sqrt(2**n) factor
         expectations = np.zeros_like(probabilities)
-        for x in range(2**boolean_circuit.num_variable_qubits):
-            bits = np.array(list(bin(x)[2:].zfill(boolean_circuit.num_variable_qubits)), dtype=int)
+        for x in range(2**boolean_object.num_variable_qubits):
+            bits = np.array(list(bin(x)[2:].zfill(boolean_object.num_variable_qubits)), dtype=int)
             result = reference(bits[::-1])
 
-            entry = int(str(int(result)) + bin(x)[2:].zfill(boolean_circuit.num_variable_qubits), 2)
-            expectations[entry] = 1 / 2**boolean_circuit.num_variable_qubits
+            entry = int(str(int(result)) + bin(x)[2:].zfill(boolean_object.num_variable_qubits), 2)
+            expectations[entry] = 1 / 2**boolean_object.num_variable_qubits
 
         np.testing.assert_array_almost_equal(probabilities, expectations)
 
@@ -63,6 +76,39 @@ def test_xor(self):
         expected.x(2)
         self.assertEqual(circuit.decompose(), expected)
 
+    def test_xor_gate(self):
+        """Test XOR-gate."""
+        xor_gate = BitwiseXorGate(num_qubits=3, amount=4)
+        expected = QuantumCircuit(3)
+        expected.x(2)
+        self.assertEqual(Operator(xor_gate), Operator(expected))
+
+    @data(
+        (5, 12),
+        (6, 21),
+    )
+    @unpack
+    def test_xor_equivalence(self, num_qubits, amount):
+        """Test that XOR-circuit and BitwiseXorGate yield equal operators."""
+        xor_gate = BitwiseXorGate(num_qubits, amount)
+        xor_circuit = XOR(num_qubits, amount)
+        self.assertEqual(Operator(xor_gate), Operator(xor_circuit))
+
+    def test_xor_eq(self):
+        """Test BitwiseXorGate's equality method."""
+        xor1 = BitwiseXorGate(num_qubits=5, amount=10)
+        xor2 = BitwiseXorGate(num_qubits=5, amount=10)
+        xor3 = BitwiseXorGate(num_qubits=5, amount=11)
+        self.assertEqual(xor1, xor2)
+        self.assertNotEqual(xor1, xor3)
+
+    def test_xor_inverse(self):
+        """Test correctness of the BitwiseXorGate's inverse."""
+        xor_gate = BitwiseXorGate(num_qubits=5, amount=10)
+        xor_gate_inverse = xor_gate.inverse()
+        self.assertEqual(xor_gate, xor_gate_inverse)
+        self.assertEqual(Operator(xor_gate), Operator(xor_gate_inverse).adjoint())
+
     def test_inner_product(self):
         """Test inner product circuit.
 
@@ -75,6 +121,22 @@ def test_inner_product(self):
         expected.cz(2, 5)
         self.assertEqual(circuit.decompose(), expected)
 
+    def test_inner_product_gate(self):
+        """Test inner product gate."""
+        inner_product = InnerProductGate(num_qubits=3)
+        expected = QuantumCircuit(6)
+        expected.cz(0, 3)
+        expected.cz(1, 4)
+        expected.cz(2, 5)
+        self.assertEqual(Operator(inner_product), Operator(expected))
+
+    @data(4, 5, 6)
+    def test_inner_product_equivalence(self, num_qubits):
+        """Test that XOR-circuit and BitwiseXorGate yield equal operators."""
+        inner_product_gate = InnerProductGate(num_qubits)
+        inner_product_circuit = InnerProduct(num_qubits)
+        self.assertEqual(Operator(inner_product_gate), Operator(inner_product_circuit))
+
     @data(
         (2, None, "noancilla"),
         (5, None, "noancilla"),
@@ -100,6 +162,57 @@ def reference(bits):
 
         self.assertBooleanFunctionIsCorrect(or_circuit, reference)
 
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_or_gate(self, num_variables, flags):
+        """Test correctness of the OrGate."""
+        or_gate = OrGate(num_variables, flags)
+        flags = flags or [1] * num_variables
+
+        def reference(bits):
+            flagged = []
+            for flag, bit in zip(flags, bits):
+                if flag < 0:
+                    flagged += [1 - bit]
+                elif flag > 0:
+                    flagged += [bit]
+            return np.any(flagged)
+
+        self.assertBooleanFunctionIsCorrect(or_gate, reference)
+
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_or_gate_inverse(self, num_variables, flags):
+        """Test correctness of the OrGate's inverse."""
+        or_gate = OrGate(num_variables, flags)
+        or_gate_inverse = or_gate.inverse()
+        self.assertEqual(Operator(or_gate), Operator(or_gate_inverse).adjoint())
+
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_or_equivalence(self, num_variables, flags):
+        """Test that OR-circuit and OrGate yield equal operators
+        (when not using ancilla qubits).
+        """
+        or_gate = OrGate(num_variables, flags)
+        or_circuit = OR(num_variables, flags)
+        self.assertEqual(Operator(or_gate), Operator(or_circuit))
+
     @data(
         (2, None, "noancilla"),
         (2, [-1, 1], "v-chain"),
@@ -108,7 +221,7 @@ def reference(bits):
     )
     @unpack
     def test_and(self, num_variables, flags, mcx_mode):
-        """Test the and circuit."""
+        """Test the AND-circuit."""
         and_circuit = AND(num_variables, flags, mcx_mode=mcx_mode)
         flags = flags or [1] * num_variables
 
@@ -123,6 +236,57 @@ def reference(bits):
 
         self.assertBooleanFunctionIsCorrect(and_circuit, reference)
 
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_and_gate(self, num_variables, flags):
+        """Test correctness of the AndGate."""
+        and_gate = AndGate(num_variables, flags)
+        flags = flags or [1] * num_variables
+
+        def reference(bits):
+            flagged = []
+            for flag, bit in zip(flags, bits):
+                if flag < 0:
+                    flagged += [1 - bit]
+                elif flag > 0:
+                    flagged += [bit]
+            return np.all(flagged)
+
+        self.assertBooleanFunctionIsCorrect(and_gate, reference)
+
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_and_gate_inverse(self, num_variables, flags):
+        """Test correctness of the AND-gate inverse."""
+        and_gate = AndGate(num_variables, flags)
+        and_gate_inverse = and_gate.inverse()
+        self.assertEqual(Operator(and_gate), Operator(and_gate_inverse).adjoint())
+
+    @data(
+        (2, None),
+        (2, [-1, 1]),
+        (5, [0, 0, -1, 1, -1]),
+        (5, [-1, 0, 0, 1, 1]),
+    )
+    @unpack
+    def test_and_equivalence(self, num_variables, flags):
+        """Test that AND-circuit and AND-gate yield equal operators
+        (when not using ancilla qubits).
+        """
+        and_gate = AndGate(num_variables, flags)
+        and_circuit = AND(num_variables, flags)
+        self.assertEqual(Operator(and_gate), Operator(and_circuit))
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/test/python/circuit/test_gate_definitions.py b/test/python/circuit/test_gate_definitions.py
index 220478159ee3..ba2546b2e8a5 100644
--- a/test/python/circuit/test_gate_definitions.py
+++ b/test/python/circuit/test_gate_definitions.py
@@ -311,6 +311,10 @@ class TestGateEquivalenceEqual(QiskitTestCase):
         "_SingletonGateOverrides",
         "_SingletonControlledGateOverrides",
         "QFTGate",
+        "AndGate",
+        "OrGate",
+        "BitwiseXorGate",
+        "InnerProductGate",
     }
 
     # Amazingly, Python's scoping rules for class bodies means that this is the closest we can get