diff --git a/qualtran/bloqs/arithmetic/addition.ipynb b/qualtran/bloqs/arithmetic/addition.ipynb
index ab22770e1..5997adc79 100644
--- a/qualtran/bloqs/arithmetic/addition.ipynb
+++ b/qualtran/bloqs/arithmetic/addition.ipynb
@@ -38,7 +38,7 @@
     "## `Add`\n",
     "An n-bit addition gate.\n",
     "\n",
-    "Implements $U|a\\rangle|b\\rangle \\rightarrow |a\\rangle|a+b\\rangle$ using $4n - 4 T$ gates.\n",
+    "Implements $U|a\\rangle|b\\rangle \\rightarrow |a\\rangle|a+b\\rangle$ using $n-1$ AND gates.\n",
     "\n",
     "#### Parameters\n",
     " - `a_dtype`: Quantum datatype used to represent the integer a.\n",
@@ -49,9 +49,81 @@
     " - `b`: A b_dtype.bitsize-sized input/output register (register b above). \n",
     "\n",
     "#### References\n",
-    " - [Halving the cost of quantum addition](https://arxiv.org/abs/1709.06648). \n"
+    " - [Halving the cost of quantum addition](https://arxiv.org/abs/1709.06648). Gidney 2018. The construction used in this bloq, evolved from [2].\n",
+    " - [A new quantum ripple-carry addition circuit](https://arxiv.org/abs/quant-ph/0410184). Cuccaro et. al. 2004.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "263c1c98-db09-4a11-bf1b-dc7426c66fce",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from qualtran import BloqBuilder\n",
+    "from qualtran.bloqs.arithmetic.addition import IdiomaticAdd, _LeftAddPart, _RightAddPart"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f30f4130-5d5b-489a-8ed9-50902ec15431",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "bb = BloqBuilder()\n",
+    "c = bb.add_register('c', 1)\n",
+    "i = bb.add_register('i', 1)\n",
+    "t = bb.add_register('t', 1)\n",
+    "c, i, t, cc = bb.add(_LeftAddPart(), c=c, i=i, t=t)\n",
+    "c, i, t = bb.add(_RightAddPart(), c=c, i=i, t=t, cc=cc)\n",
+    "cbloq = bb.finalize(c=c, i=i, t=t)\n",
+    "show_bloq(cbloq, 'musical_score')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "13bc1255-8e3c-49f6-8c1f-c174ae64cdc8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "show_bloq(cbloq.flatten_once(lambda b: True), 'musical_score')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "77d8cfcf-bae6-4420-a145-729622da23e0",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m = IdiomaticAdd(5)\n",
+    "cm = m.decompose_bloq()\n",
+    "show_bloq(cm, 'musical_score')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "08645d99-8f4e-4324-9028-9401911228c7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%time\n",
+    "m = IdiomaticAdd(10_000)\n",
+    "cbloq = m.decompose_bloq()\n",
+    "print(cbloq._binst_graph.number_of_nodes())"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "42153aa5-d2fa-46a7-b2f1-9720ef5db669",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -95,7 +167,17 @@
    },
    "outputs": [],
    "source": [
-    "add_large = Add(QUInt(bitsize=64))"
+    "add_large = Add(QUInt(bitsize=5000))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cbc705bc-b7cb-4f32-b3ba-0410f45f15cb",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "add_large.decompose_bloq()"
    ]
   },
   {
@@ -116,7 +198,10 @@
    "execution_count": null,
    "id": "e5b746c1",
    "metadata": {
-    "collapsed": false
+    "collapsed": false,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -337,7 +422,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cd255bf9",
+   "id": "47b4b6d7",
    "metadata": {
     "cq.autogen": "AddK.bloq_doc.py"
    },
@@ -348,7 +433,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7538f9a5",
+   "id": "7152a86b",
    "metadata": {
     "cq.autogen": "AddK.example_instances.md"
    },
@@ -359,7 +444,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4305289f",
+   "id": "a50b7ae4",
    "metadata": {
     "cq.autogen": "AddK.add_k"
    },
@@ -372,7 +457,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6048819",
+   "id": "7f7e9c09",
    "metadata": {
     "cq.autogen": "AddK.add_k_small"
    },
@@ -384,7 +469,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b67fd469",
+   "id": "802f8da2",
    "metadata": {
     "cq.autogen": "AddK.add_k_large"
    },
@@ -395,7 +480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8b04228",
+   "id": "21737304",
    "metadata": {
     "cq.autogen": "AddK.graphical_signature.md"
    },
@@ -406,7 +491,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e93e7f2e",
+   "id": "1849daf3",
    "metadata": {
     "cq.autogen": "AddK.graphical_signature.py"
    },
@@ -419,7 +504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "13552795",
+   "id": "83759458",
    "metadata": {
     "cq.autogen": "AddK.call_graph.md"
    },
@@ -430,7 +515,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d8d6584e",
+   "id": "a3c60bc5",
    "metadata": {
     "cq.autogen": "AddK.call_graph.py"
    },
@@ -471,7 +556,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.11.7"
+   "version": "3.11.8"
   }
  },
  "nbformat": 4,
diff --git a/qualtran/bloqs/arithmetic/addition.py b/qualtran/bloqs/arithmetic/addition.py
index c1965bba2..584478bca 100644
--- a/qualtran/bloqs/arithmetic/addition.py
+++ b/qualtran/bloqs/arithmetic/addition.py
@@ -57,6 +57,7 @@
 )
 from qualtran.bloqs import util_bloqs
 from qualtran.bloqs.basic_gates import CNOT, XGate
+from qualtran.bloqs.mcmt import MultiTargetCNOT
 from qualtran.bloqs.mcmt.and_bloq import And
 from qualtran.bloqs.mcmt.multi_control_multi_target_pauli import MultiControlX
 from qualtran.cirq_interop import decompose_from_cirq_style_method
@@ -73,6 +74,82 @@
     from qualtran.symbolics import SymbolicInt
 
 
+@frozen
+class _LeftAddPart(Bloq):
+    """The 'left' part of the addition building block from the reference, figure 2."""
+
+    @property
+    def signature(self) -> Signature:
+        return Signature(
+            [
+                Register('c', QUInt(1)),
+                Register('i', QUInt(1)),
+                Register('t', QUInt(1)),
+                Register('out', QUInt(1), side=Side.RIGHT),
+            ]
+        )
+
+    def build_composite_bloq(self, bb: 'BloqBuilder', c, i, t) -> Dict[str, 'SoquetT']:
+        c, [i, t] = bb.add(MultiTargetCNOT(2), ctrl=c, targets=[i, t])
+        [i, t], out = bb.add(And(), ctrl=[i, t])
+        c, out = bb.add(CNOT(), ctrl=c, target=out)
+        return {'c': c, 'i': i, 't': t, 'out': out}
+
+
+@frozen
+class _RightAddPart(Bloq):
+    """The 'right' part of the addition building block from the reference, figure 2."""
+
+    @property
+    def signature(self) -> 'Signature':
+        return Signature(
+            [
+                Register('c', QUInt(1)),
+                Register('i', QUInt(1)),
+                Register('t', QUInt(1)),
+                Register('cc', QUInt(1), side=Side.LEFT),
+            ]
+        )
+
+    def build_composite_bloq(self, bb: 'BloqBuilder', c, i, t, cc) -> Dict[str, 'SoquetT']:
+        c, cc = bb.add(CNOT(), ctrl=c, target=cc)
+        i, t = bb.add(And().adjoint(), ctrl=[i, t], target=cc)
+        c, i = bb.add(CNOT(), ctrl=c, target=i)
+        i, t = bb.add(CNOT(), ctrl=i, target=t)
+        return {'c': c, 'i': i, 't': t}
+
+
+@frozen
+class IdiomaticAdd(Bloq):
+    """An addition circuit; follows figure 1"""
+
+    n: 'SymbolicInt'
+
+    @property
+    def signature(self) -> Signature:
+        return Signature([Register('a', QUInt(self.n)), Register('b', QUInt(self.n))])
+
+    def build_composite_bloq(self, bb: 'BloqBuilder', a, b) -> Dict[str, 'SoquetT']:
+        a_bits = bb.split(a)
+        b_bits = bb.split(b)
+        anc = bb.allocate(1)
+        ancs = [anc]
+
+        for i in range(self.n):
+            ancs[-1], a_bits[i], b_bits[i], anc = bb.add(
+                _LeftAddPart(), c=ancs[-1], i=a_bits[i], t=b_bits[i]
+            )
+            ancs.append(anc)
+
+        for i in range(self.n - 1, -1, -1):
+            ancs[i], a_bits[i], b_bits[i] = bb.add(
+                _RightAddPart(), c=ancs[i], i=a_bits[i], t=b_bits[i], cc=ancs[i + 1]
+            )
+
+        bb.free(ancs[0])
+        return {'a': bb.join(a_bits), 'b': bb.join(b_bits)}
+
+
 @frozen
 class Add(Bloq):
     r"""An n-bit addition gate.
diff --git a/qualtran/bloqs/mcmt/multi_control_multi_target_pauli.py b/qualtran/bloqs/mcmt/multi_control_multi_target_pauli.py
index 92cbd2434..11629a28e 100644
--- a/qualtran/bloqs/mcmt/multi_control_multi_target_pauli.py
+++ b/qualtran/bloqs/mcmt/multi_control_multi_target_pauli.py
@@ -60,7 +60,9 @@ class MultiTargetCNOT(GateWithRegisters):
 
     @cached_property
     def signature(self) -> Signature:
-        return Signature.build(control=1, targets=self.bitsize)
+        return Signature(
+            [Register('ctrl', QBit()), Register('targets', QBit(), shape=(self.bitsize,))]
+        )
 
     def decompose_from_registers(
         self,