diff --git a/qualtran/bloqs/arithmetic/controlled_addition.py b/qualtran/bloqs/arithmetic/controlled_addition.py
new file mode 100644
index 000000000..15dd23100
--- /dev/null
+++ b/qualtran/bloqs/arithmetic/controlled_addition.py
@@ -0,0 +1,231 @@
+#  Copyright 2024 Google LLC
+#
+#  Licensed under the Apache License, Version 2.0 (the "License");
+#  you may not use this file except in compliance with the License.
+#  You may obtain a copy of the License at
+#
+#      https://www.apache.org/licenses/LICENSE-2.0
+#
+#  Unless required by applicable law or agreed to in writing, software
+#  distributed under the License is distributed on an "AS IS" BASIS,
+#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#  See the License for the specific language governing permissions and
+#  limitations under the License.
+import itertools
+import math
+from typing import Any, Dict, Iterator, Set, TYPE_CHECKING, Union
+
+import cirq
+import numpy as np
+import sympy
+from attrs import field, frozen
+from numpy.typing import NDArray
+
+from qualtran import Bloq, CompositeBloq, QBit, QInt, QUInt, Register, Signature, Soquet, SoquetT
+from qualtran._infra.data_types import QMontgomeryUInt
+from qualtran.bloqs.basic_gates import CNOT
+from qualtran.bloqs.mcmt import MultiControlX
+from qualtran.bloqs.mcmt.and_bloq import And
+from qualtran.cirq_interop import decompose_from_cirq_style_method
+from qualtran.cirq_interop.t_complexity_protocol import TComplexity
+
+if TYPE_CHECKING:
+    import quimb.tensor as qtn
+
+    from qualtran.drawing import WireSymbol
+    from qualtran.resource_counting import BloqCountT, SympySymbolAllocator
+    from qualtran.simulation.classical_sim import ClassicalValT
+
+
+@frozen
+class CAdd(Bloq):
+    r"""An n-bit controlled-addition gate.
+
+    Args:
+        a_dtype: Quantum datatype used to represent the integer a.
+        b_dtype: Quantum datatype used to represent the integer b. Must be large
+            enough to hold the result in the output register of a + b, or else it simply
+            drops the most significant bits. If not specified, b_dtype is set to a_dtype.
+        cv: When controlled=0, this bloq is active when the ctrl register is 0. When
+            controlled=1, this bloq is active when the ctrl register is 1.
+
+    Registers:
+        ctrl: the control bit for the addition
+        a: A a_dtype.bitsize-sized input register (register a above).
+        b: A b_dtype.bitsize-sized input/output register (register b above).
+
+    References:
+        [Halving the cost of quantum addition](https://arxiv.org/abs/1709.06648)
+    """
+
+    a_dtype: Union[QInt, QUInt, QMontgomeryUInt] = field()
+    b_dtype: Union[QInt, QUInt, QMontgomeryUInt] = field()
+    cv: int = field(default=1)
+
+    @b_dtype.default
+    def b_dtype_default(self):
+        return self.a_dtype
+
+    @a_dtype.validator
+    def _a_dtype_validate(self, field, val):
+        if not isinstance(val, (QInt, QUInt, QMontgomeryUInt)):
+            raise ValueError("Only QInt, QUInt and QMontgomerUInt types are supported.")
+        if isinstance(val.num_qubits, sympy.Expr):
+            return
+        if val.bitsize > self.b_dtype.bitsize:
+            raise ValueError("a_dtype bitsize must be less than or equal to b_dtype bitsize")
+
+    @b_dtype.validator
+    def _b_dtype_validate(self, field, val):
+        if not isinstance(val, (QInt, QUInt, QMontgomeryUInt)):
+            raise ValueError("Only QInt, QUInt and QMontgomerUInt types are supported.")
+
+    @cv.validator
+    def _controlled_validate(self, field, val):
+        if val not in (0, 1):
+            raise ValueError("controlled must be either 0 or 1")
+
+    @property
+    def signature(self):
+        return Signature(
+            [Register("ctrl", QBit()), Register("a", self.a_dtype), Register("b", self.b_dtype)]
+        )
+
+    def add_my_tensors(
+        self,
+        tn: 'qtn.TensorNetwork',
+        tag: Any,
+        *,
+        incoming: Dict[str, 'SoquetT'],
+        outgoing: Dict[str, 'SoquetT'],
+    ):
+        import quimb.tensor as qtn
+
+        if isinstance(self.a_dtype, QInt) or isinstance(self.b_dtype, QInt):
+            raise TypeError("Tensor contraction for addition is only supported for unsigned ints.")
+        N_a = 2**self.a_dtype.bitsize
+        N_b = 2**self.b_dtype.bitsize
+        inds = (
+            incoming['ctrl'],
+            incoming['a'],
+            incoming['b'],
+            outgoing['ctrl'],
+            outgoing['a'],
+            outgoing['b'],
+        )
+        unitary = np.zeros((2, N_a, N_b, 2, N_a, N_b), dtype=np.complex128)
+        for c, a, b in itertools.product(range(2), range(N_a), range(N_b)):
+            if c == self.cv:
+                unitary[c, a, b, c, a, int(math.fmod(a + b, N_b))] = 1
+            else:
+                unitary[c, a, b, c, a, b] = 1
+
+        tn.add(qtn.Tensor(data=unitary, inds=inds, tags=[self.short_name(), tag]))
+
+    def decompose_bloq(self) -> 'CompositeBloq':
+        return decompose_from_cirq_style_method(self)
+
+    def on_classical_vals(self, **kwargs) -> Dict[str, 'ClassicalValT']:
+        a, b = kwargs['a'], kwargs['b']
+        unsigned = isinstance(self.a_dtype, (QUInt, QMontgomeryUInt))
+        b_bitsize = self.b_dtype.bitsize
+        N = 2**b_bitsize if unsigned else 2 ** (b_bitsize - 1)
+        ctrl = kwargs['ctrl']
+        if ctrl != self.cv:
+            return {'ctrl': ctrl, 'a': a, 'b': b}
+        else:
+            return {'ctrl': ctrl, 'a': a, 'b': int(math.fmod(a + b, N))}
+
+    def short_name(self) -> str:
+        return "a+b"
+
+    def wire_symbol(self, soq: 'Soquet') -> 'WireSymbol':
+        from qualtran.drawing import directional_text_box
+
+        if soq.reg.name == 'ctrl':
+            return directional_text_box('ctrl', side=soq.reg.side)
+        if soq.reg.name == 'a':
+            return directional_text_box('a', side=soq.reg.side)
+        elif soq.reg.name == 'b':
+            return directional_text_box('a+b', side=soq.reg.side)
+        else:
+            raise ValueError()
+
+    def _left_building_block(self, inp, out, anc, depth):
+        if depth == self.b_dtype.bitsize - 1:
+            return
+        else:
+            if depth < 1:
+                raise ValueError(f"{depth=} is not a positive integer")
+            if depth < len(inp):
+                yield CNOT().on(anc[depth - 1], inp[depth])
+                control = inp[depth]
+            else:
+                # If inp[depth] doesn't exist, we treat it as a |0>,
+                # and therefore applying CNOT().on(anc[depth - 1], inp[depth])
+                # essentially "copies" anc[depth - 1] into inp[depth]
+                # in the classical basis. So therefore, on future operations,
+                # we can use anc[depth - 1] in its place.
+                control = anc[depth - 1]
+            yield CNOT().on(anc[depth - 1], out[depth])
+            yield And().on(control, out[depth], anc[depth])
+            yield CNOT().on(anc[depth - 1], anc[depth])
+            yield from self._left_building_block(inp, out, anc, depth + 1)
+
+    def _right_building_block(self, inp, out, anc, control, depth):
+        if depth == 0:
+            return
+        yield CNOT().on(anc[depth - 1], anc[depth])
+        if depth < len(inp):
+            yield And().adjoint().on(inp[depth], out[depth], anc[depth])
+            yield MultiControlX((1, 1)).on(control, inp[depth], out[depth])
+            yield CNOT().on(anc[depth - 1], inp[depth])
+        else:
+            yield And().adjoint().on(anc[depth - 1], out[depth], anc[depth])
+            yield MultiControlX((1, 1)).on(control, anc[depth - 1], out[depth])
+        yield CNOT().on(anc[depth - 1], out[depth])
+        yield from self._right_building_block(inp, out, anc, control, depth - 1)
+
+    def decompose_from_registers(
+        self, *, context: cirq.DecompositionContext, **quregs: NDArray[cirq.Qid]  # type: ignore[type-var]
+    ) -> Iterator[cirq.OP_TREE]:
+        # reverse the order of qubits for big endian-ness.
+        input_bits = quregs['a'][::-1]
+        output_bits = quregs['b'][::-1]
+        ancillas = context.qubit_manager.qalloc(self.b_dtype.bitsize - 1)[::-1]
+        control = quregs['ctrl'][0]
+        if self.cv == 0:
+            yield cirq.X(control)
+        # Start off the addition by anding into the ancilla
+        yield And().on(input_bits[0], output_bits[0], ancillas[0])
+        # Left part of Fig.4
+        yield from self._left_building_block(input_bits, output_bits, ancillas, 1)
+        yield CNOT().on(ancillas[-1], output_bits[-1])
+        if len(input_bits) == len(output_bits):
+            yield MultiControlX((1, 1)).on(control, input_bits[-1], output_bits[-1])
+            yield CNOT().on(ancillas[-1], output_bits[-1])
+        # right part of Fig.4
+        yield from self._right_building_block(
+            input_bits, output_bits, ancillas, control, self.b_dtype.bitsize - 2
+        )
+        yield And().adjoint().on(input_bits[0], output_bits[0], ancillas[0])
+        yield MultiControlX((1, 1)).on(control, input_bits[0], output_bits[0])
+        if self.cv == 0:
+            yield cirq.X(control)
+        context.qubit_manager.qfree(ancillas)
+
+    def _t_complexity_(self):
+        n = self.b_dtype.bitsize
+        num_and = 2 * n - 1
+        num_clifford = 33 * (n - 2) + 43
+        return TComplexity(t=4 * num_and, clifford=num_clifford)
+
+    def build_call_graph(self, ssa: 'SympySymbolAllocator') -> Set['BloqCountT']:
+        n = self.b_dtype.bitsize
+        n_cnot = (n - 2) * 6 + 2
+        return {
+            (MultiControlX((1, 1)), n),
+            (And(), n - 1),
+            (And().adjoint(), n - 1),
+            (CNOT(), n_cnot),
+        }
diff --git a/qualtran/bloqs/arithmetic/controlled_addition_test.py b/qualtran/bloqs/arithmetic/controlled_addition_test.py
new file mode 100644
index 000000000..abfa4a1c2
--- /dev/null
+++ b/qualtran/bloqs/arithmetic/controlled_addition_test.py
@@ -0,0 +1,74 @@
+#  Copyright 2024 Google LLC
+#
+#  Licensed under the Apache License, Version 2.0 (the "License");
+#  you may not use this file except in compliance with the License.
+#  You may obtain a copy of the License at
+#
+#      https://www.apache.org/licenses/LICENSE-2.0
+#
+#  Unless required by applicable law or agreed to in writing, software
+#  distributed under the License is distributed on an "AS IS" BASIS,
+#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#  See the License for the specific language governing permissions and
+#  limitations under the License.
+
+import cirq
+import numpy as np
+import pytest
+
+import qualtran.testing as qlt_testing
+from qualtran import QUInt
+from qualtran.bloqs.arithmetic.controlled_addition import CAdd
+from qualtran.cirq_interop.testing import assert_circuit_inp_out_cirqsim
+from qualtran.resource_counting.generalizers import ignore_split_join
+
+
+def iter_bits(x, w):
+    return [int(b) for b in np.binary_repr(x, width=w)]
+
+
+@pytest.mark.parametrize('a', [1, 2])
+@pytest.mark.parametrize('b', [1, 2, 3])
+@pytest.mark.parametrize('num_bits_a', [2, 3])
+@pytest.mark.parametrize('num_bits_b', [5])
+@pytest.mark.parametrize('controlled_on', [0, 1])
+@pytest.mark.parametrize('control', [0, 1])
+def test_controlled_addition(a, b, num_bits_a, num_bits_b, controlled_on, control):
+    num_anc = num_bits_b - 1
+    gate = CAdd(QUInt(num_bits_a), QUInt(num_bits_b), cv=controlled_on)
+    qubits = cirq.LineQubit.range(num_bits_a + num_bits_b + 1)
+    op = gate.on_registers(ctrl=qubits[0], a=qubits[1 : num_bits_a + 1], b=qubits[num_bits_a + 1 :])
+    greedy_mm = cirq.GreedyQubitManager(prefix="_a", maximize_reuse=True)
+    context = cirq.DecompositionContext(greedy_mm)
+    circuit = cirq.Circuit(cirq.decompose_once(op, context=context))
+    circuit0 = cirq.Circuit(op)
+    ancillas = sorted(circuit.all_qubits())[-num_anc:]
+    initial_state = [0] * (num_bits_a + num_bits_b + num_anc + 1)
+    initial_state[0] = control
+    initial_state[1 : num_bits_a + 1] = list(iter_bits(a, num_bits_a))
+    initial_state[num_bits_a + 1 : num_bits_a + num_bits_b + 1] = list(iter_bits(b, num_bits_b))
+    final_state = [0] * (num_bits_a + num_bits_b + num_anc + 1)
+    final_state[0] = control
+    final_state[1 : num_bits_a + 1] = list(iter_bits(a, num_bits_a))
+    if control == controlled_on:
+        final_state[num_bits_a + 1 : num_bits_a + num_bits_b + 1] = list(
+            iter_bits(a + b, num_bits_b)
+        )
+    else:
+        final_state[num_bits_a + 1 : num_bits_a + num_bits_b + 1] = list(iter_bits(b, num_bits_b))
+    assert_circuit_inp_out_cirqsim(circuit, qubits + ancillas, initial_state, final_state)
+    assert_circuit_inp_out_cirqsim(
+        circuit0, qubits, initial_state[:-num_anc], final_state[:-num_anc]
+    )
+
+
+@pytest.mark.parametrize("n", [*range(3, 10)])
+def test_addition_gate_counts_controlled(n: int):
+    add = CAdd(QUInt(n), cv=1)
+    num_and = 2 * n - 1
+    t_count = 4 * num_and
+
+    qlt_testing.assert_valid_bloq_decomposition(add)
+    assert add.t_complexity() == add.decompose_bloq().t_complexity()
+    assert add.bloq_counts() == add.decompose_bloq().bloq_counts(generalizer=ignore_split_join)
+    assert add.t_complexity().t == t_count