diff --git a/cirq-core/cirq/__init__.py b/cirq-core/cirq/__init__.py
index 59264fe3bb4..ae2bf4f457f 100644
--- a/cirq-core/cirq/__init__.py
+++ b/cirq-core/cirq/__init__.py
@@ -196,6 +196,7 @@
     bit_flip,
     BitFlipChannel,
     BooleanHamiltonian,
+    BooleanHamiltonianGate,
     CCX,
     CCXPowGate,
     CCZ,
diff --git a/cirq-core/cirq/json_resolver_cache.py b/cirq-core/cirq/json_resolver_cache.py
index 44ece45bc90..f15252c3256 100644
--- a/cirq-core/cirq/json_resolver_cache.py
+++ b/cirq-core/cirq/json_resolver_cache.py
@@ -59,6 +59,7 @@ def _parallel_gate_op(gate, qubits):
         'BitFlipChannel': cirq.BitFlipChannel,
         'BitstringAccumulator': cirq.work.BitstringAccumulator,
         'BooleanHamiltonian': cirq.BooleanHamiltonian,
+        'BooleanHamiltonianGate': cirq.BooleanHamiltonianGate,
         'CCNotPowGate': cirq.CCNotPowGate,
         'CCXPowGate': cirq.CCXPowGate,
         'CCZPowGate': cirq.CCZPowGate,
diff --git a/cirq-core/cirq/ops/__init__.py b/cirq-core/cirq/ops/__init__.py
index 552b5a7119e..5ff9c8f4baa 100644
--- a/cirq-core/cirq/ops/__init__.py
+++ b/cirq-core/cirq/ops/__init__.py
@@ -32,6 +32,7 @@
 
 from cirq.ops.boolean_hamiltonian import (
     BooleanHamiltonian,
+    BooleanHamiltonianGate,
 )
 
 from cirq.ops.common_channels import (
diff --git a/cirq-core/cirq/ops/boolean_hamiltonian.py b/cirq-core/cirq/ops/boolean_hamiltonian.py
index 2e92e577e75..f4fbf019d6c 100644
--- a/cirq-core/cirq/ops/boolean_hamiltonian.py
+++ b/cirq-core/cirq/ops/boolean_hamiltonian.py
@@ -22,19 +22,20 @@
 [4] Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas by Jonathan Welch, Daniel
     Greenbaum, Sarah Mostame, and Alán Aspuru-Guzik, https://arxiv.org/abs/1306.3991
 """
-import itertools
 import functools
-
+import itertools
 from typing import Any, Dict, Generator, List, Sequence, Tuple
 
 import sympy.parsing.sympy_parser as sympy_parser
 
 import cirq
 from cirq import value
+from cirq._compat import deprecated_class
 from cirq.ops import raw_types
 from cirq.ops.linear_combinations import PauliSum, PauliString
 
 
+@deprecated_class(deadline='v0.15', fix='Use cirq.BooleanHamiltonianGate')
 @value.value_equality
 class BooleanHamiltonian(raw_types.Operation):
     """An operation that represents a Hamiltonian from a set of Boolean functions."""
@@ -64,7 +65,12 @@ def __init__(
             boolean_strs: The list of Sympy-parsable Boolean expressions.
             qubit_map: map of string (boolean variable name) to qubit.
             theta: The evolution time (angle) for the Hamiltonian
+
+        Raises:
+            ValueError: If the any qubits are not 2D.
         """
+        if any(q.dimension != 2 for q in qubit_map.values()):
+            raise ValueError('All qubits must be 2-dimensional.')
         self._qubit_map: Dict[str, 'cirq.Qid'] = qubit_map
         self._boolean_strs: Sequence[str] = boolean_strs
         self._theta: float = theta
@@ -114,6 +120,91 @@ def _decompose_(self):
             hamiltonian_polynomial_list, self._qubit_map, self._theta
         )
 
+    def _has_unitary_(self):
+        return True
+
+    @property
+    def gate(self) -> 'cirq.Gate':
+        return BooleanHamiltonianGate(
+            tuple(self._qubit_map.keys()), self._boolean_strs, self._theta
+        )
+
+
+@value.value_equality
+class BooleanHamiltonianGate(raw_types.Gate):
+    """A gate that represents a Hamiltonian from a set of Boolean functions."""
+
+    def __init__(
+        self,
+        parameter_names: Sequence[str],
+        boolean_strs: Sequence[str],
+        theta: float,
+    ):
+        """Builds a BooleanHamiltonianGate.
+
+        For each element of a sequence of Boolean expressions, the code first transforms it into a
+        polynomial of Pauli Zs that represent that particular expression. Then, we sum all the
+        polynomials, thus making a function that goes from a series to Boolean inputs to an integer
+        that is the number of Boolean expressions that are true.
+
+        For example, if we were using this gate for the unweighted max-cut problem that is typically
+        used to demonstrate the QAOA algorithm, there would be one Boolean expression per edge. Each
+        Boolean expression would be true iff the vertices on that are in different cuts (i.e. it's)
+        an XOR.
+
+        Then, we compute exp(-j * theta * polynomial), which is unitary because the polynomial is
+        Hermitian.
+
+        Args:
+            parameter_names: The names of the inputs to the expressions.
+            boolean_strs: The list of Sympy-parsable Boolean expressions.
+            theta: The evolution time (angle) for the Hamiltonian
+        """
+        self._parameter_names: Sequence[str] = parameter_names
+        self._boolean_strs: Sequence[str] = boolean_strs
+        self._theta: float = theta
+
+    def _qid_shape_(self) -> Tuple[int, ...]:
+        return (2,) * len(self._parameter_names)
+
+    def _value_equality_values_(self) -> Any:
+        return self._parameter_names, self._boolean_strs, self._theta
+
+    def _json_dict_(self) -> Dict[str, Any]:
+        return {
+            'cirq_type': self.__class__.__name__,
+            'parameter_names': self._parameter_names,
+            'boolean_strs': self._boolean_strs,
+            'theta': self._theta,
+        }
+
+    @classmethod
+    def _from_json_dict_(
+        cls, parameter_names, boolean_strs, theta, **kwargs
+    ) -> 'cirq.BooleanHamiltonianGate':
+        return cls(parameter_names, boolean_strs, theta)
+
+    def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
+        qubit_map = dict(zip(self._parameter_names, qubits))
+        boolean_exprs = [sympy_parser.parse_expr(boolean_str) for boolean_str in self._boolean_strs]
+        hamiltonian_polynomial_list = [
+            PauliSum.from_boolean_expression(boolean_expr, qubit_map)
+            for boolean_expr in boolean_exprs
+        ]
+
+        return _get_gates_from_hamiltonians(hamiltonian_polynomial_list, qubit_map, self._theta)
+
+    def _has_unitary_(self) -> bool:
+        return True
+
+    def __repr__(self) -> str:
+        return (
+            f'cirq.BooleanHamiltonianGate('
+            f'parameter_names={self._parameter_names!r}, '
+            f'boolean_strs={self._boolean_strs!r}, '
+            f'theta={self._theta!r})'
+        )
+
 
 def _gray_code_comparator(k1: Tuple[int, ...], k2: Tuple[int, ...], flip: bool = False) -> int:
     """Compares two Gray-encoded binary numbers.
diff --git a/cirq-core/cirq/ops/boolean_hamiltonian_test.py b/cirq-core/cirq/ops/boolean_hamiltonian_test.py
index a7c5c65eee7..4932450836d 100644
--- a/cirq-core/cirq/ops/boolean_hamiltonian_test.py
+++ b/cirq-core/cirq/ops/boolean_hamiltonian_test.py
@@ -53,7 +53,8 @@
         '(x2 | x1) ^ x0',
     ],
 )
-def test_circuit(boolean_str):
+@pytest.mark.parametrize('transform', [lambda op: op, lambda op: op.gate.on(*op.qubits)])
+def test_circuit(boolean_str, transform):
     boolean_expr = sympy_parser.parse_expr(boolean_str)
     var_names = cirq.parameter_names(boolean_expr)
     qubits = [cirq.NamedQubit(name) for name in var_names]
@@ -72,13 +73,14 @@ def test_circuit(boolean_str):
     circuit = cirq.Circuit()
     circuit.append(cirq.H.on_each(*qubits))
 
-    hamiltonian_gate = cirq.BooleanHamiltonian(
-        {q.name: q for q in qubits}, [boolean_str], 0.1 * math.pi
-    )
+    with cirq.testing.assert_deprecated('Use cirq.BooleanHamiltonianGate', deadline='v0.15'):
+        hamiltonian_gate = cirq.BooleanHamiltonian(
+            {q.name: q for q in qubits}, [boolean_str], 0.1 * math.pi
+        )
 
     assert hamiltonian_gate.num_qubits() == n
 
-    circuit.append(hamiltonian_gate)
+    circuit.append(transform(hamiltonian_gate))
 
     phi = cirq.Simulator().simulate(circuit, qubit_order=qubits, initial_state=0).state_vector()
     actual = np.arctan2(phi.real, phi.imag) - math.pi / 2.0 > 0.0
@@ -89,18 +91,53 @@ def test_circuit(boolean_str):
 
 def test_with_custom_names():
     q0, q1, q2, q3 = cirq.LineQubit.range(4)
-    original_op = cirq.BooleanHamiltonian(
-        {'a': q0, 'b': q1},
+    with cirq.testing.assert_deprecated(
+        'Use cirq.BooleanHamiltonianGate', deadline='v0.15', count=3
+    ):
+        original_op = cirq.BooleanHamiltonian(
+            {'a': q0, 'b': q1},
+            ['a'],
+            0.1,
+        )
+        assert cirq.decompose(original_op) == [cirq.Rz(rads=-0.05).on(q0)]
+
+        renamed_op = original_op.with_qubits(q2, q3)
+        assert cirq.decompose(renamed_op) == [cirq.Rz(rads=-0.05).on(q2)]
+
+        with pytest.raises(ValueError, match='Length of replacement qubits must be the same'):
+            original_op.with_qubits(q2)
+
+        with pytest.raises(ValueError, match='All qubits must be 2-dimensional'):
+            original_op.with_qubits(q0, cirq.LineQid(1, 3))
+
+
+def test_gate_with_custom_names():
+    q0, q1, q2, q3 = cirq.LineQubit.range(4)
+    gate = cirq.BooleanHamiltonianGate(
+        ['a', 'b'],
         ['a'],
         0.1,
     )
-    assert cirq.decompose(original_op) == [cirq.Rz(rads=-0.05).on(q0)]
+    assert cirq.decompose(gate.on(q0, q1)) == [cirq.Rz(rads=-0.05).on(q0)]
+    assert cirq.decompose_once_with_qubits(gate, (q0, q1)) == [cirq.Rz(rads=-0.05).on(q0)]
+    assert cirq.decompose(gate.on(q2, q3)) == [cirq.Rz(rads=-0.05).on(q2)]
+    assert cirq.decompose_once_with_qubits(gate, (q2, q3)) == [cirq.Rz(rads=-0.05).on(q2)]
+
+    with pytest.raises(ValueError, match='Wrong number of qubits'):
+        gate.on(q2)
+    with pytest.raises(ValueError, match='Wrong shape of qids'):
+        gate.on(q0, cirq.LineQid(1, 3))
 
-    renamed_op = original_op.with_qubits(q2, q3)
-    assert cirq.decompose(renamed_op) == [cirq.Rz(rads=-0.05).on(q2)]
 
-    with pytest.raises(ValueError, match='Length of replacement qubits must be the same'):
-        original_op.with_qubits(q2)
+def test_gate_consistent():
+    gate = cirq.BooleanHamiltonianGate(
+        ['a', 'b'],
+        ['a'],
+        0.1,
+    )
+    op = gate.on(*cirq.LineQubit.range(2))
+    cirq.testing.assert_implements_consistent_protocols(gate)
+    cirq.testing.assert_implements_consistent_protocols(op)
 
 
 @pytest.mark.parametrize(
diff --git a/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.json b/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.json
new file mode 100644
index 00000000000..23d6e7a221b
--- /dev/null
+++ b/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.json
@@ -0,0 +1,8 @@
+[
+  {
+    "cirq_type": "BooleanHamiltonianGate",
+    "parameter_names": ["q0", "q1"],
+    "boolean_strs": ["q0"],
+    "theta": 0.20160913
+  }
+]
\ No newline at end of file
diff --git a/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.repr b/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.repr
new file mode 100644
index 00000000000..0d1c4055ad9
--- /dev/null
+++ b/cirq-core/cirq/protocols/json_test_data/BooleanHamiltonianGate.repr
@@ -0,0 +1 @@
+[cirq.BooleanHamiltonianGate(parameter_names=['q0', 'q1'], boolean_strs=['q0'], theta=0.20160913)]
\ No newline at end of file
diff --git a/cirq-core/cirq/protocols/json_test_data/spec.py b/cirq-core/cirq/protocols/json_test_data/spec.py
index 98f3e7b13da..f23a193d5ac 100644
--- a/cirq-core/cirq/protocols/json_test_data/spec.py
+++ b/cirq-core/cirq/protocols/json_test_data/spec.py
@@ -190,6 +190,7 @@
     ],
     deprecated={
         'GlobalPhaseOperation': 'v0.16',
+        'BooleanHamiltonian': 'v0.15',
         'SymmetricalQidPair': 'v0.15',
     },
     tested_elsewhere=[