diff --git a/qualtran/quirk_interop/bloq_to_quirk.py b/qualtran/quirk_interop/bloq_to_quirk.py
new file mode 100644
index 000000000..7cb469b88
--- /dev/null
+++ b/qualtran/quirk_interop/bloq_to_quirk.py
@@ -0,0 +1,143 @@
+import subprocess
+from typing import Optional
+
+from qualtran import Bloq, DecomposeTypeError, CompositeBloq
+from qualtran.bloqs.bookkeeping import Join, Split
+from qualtran.drawing import (
+    ModPlus,
+    Circle,
+    LarrowTextBox,
+    RarrowTextBox,
+    LineManager,
+    get_musical_score_data,
+)
+from qualtran.drawing.musical_score import _cbloq_musical_score
+
+
+class SparseLineManager(LineManager):
+    """
+    LineManager which keeps partitioned line slots reserved for them until they need it again
+
+    # DIDN'TDO: only handles partition patterns of the type (QAny(n)/QUInt(n)/... -> QBit((n,))
+    # or QBit((n,)) -> QAny(n))
+    """
+
+    def __init__(self, cbloq: CompositeBloq, max_n_lines: int = 100):
+        super().__init__(max_n_lines)
+        # Pre-layout pass with a plain LineManager, used only to infer Join/Split pairing.
+        _, self.soq_assign, _ = _cbloq_musical_score(
+            cbloq.signature, binst_graph=cbloq._binst_graph, manager=LineManager()
+        )
+        self._join_to_split_id = self._build_join_to_split_map()
+        self._split_to_join_id = self._build_split_to_join_map()
+
+    def _find_dual_on_line(self, line: int, start: int, dual_cls: Bloq):
+        dual_candidates = [
+            (rpos.seq_x, soq.binst.i)  # type: ignore[union-attr]
+            for soq, rpos in self.soq_assign.items()
+            if rpos.y == line and rpos.seq_x > start and soq.binst.bloq_is(dual_cls)
+        ]
+        if not dual_candidates:
+            return None
+        dual_candidates.sort(key=lambda x: x[0])
+        return dual_candidates[0][1]
+
+    def _build_join_to_split_map(self):
+        join_to_split = {}
+        for soq, rpos in self.soq_assign.items():
+            if soq.binst.bloq_is(Join) and soq.idx == ():
+                dual_id = self._find_dual_on_line(rpos.y, rpos.seq_x, Split)
+                if dual_id is not None:
+                    join_to_split[soq.binst.i] = dual_id  # type: ignore[union-attr]
+        return join_to_split
+
+    def _build_split_to_join_map(self):
+        split_to_join = {}
+        for soq, rpos in self.soq_assign.items():
+            if soq.binst.bloq_is(Split) and soq.idx != ():
+                dual_id = self._find_dual_on_line(rpos.y, rpos.seq_x, Join)
+                if dual_id is not None:
+                    split_to_join[soq.binst.i] = dual_id  # type: ignore[union-attr]
+        return split_to_join
+
+    def maybe_reserve(self, binst, reg, idx):
+        # Reserve one slot so a partitioned wire can reclaim the same vertical region
+        # at its dual Join/Split.
+        if binst.bloq_is(Join) and reg.shape:
+            dual_id = self._join_to_split_id.get(binst.i)
+            self.reserve_n(1, lambda binst_to_check, reg_to_check: binst_to_check.i == dual_id)
+
+        if binst.bloq_is(Split) and not reg.shape:
+            dual_id = self._split_to_join_id.get(binst.i)
+            self.reserve_n(1, lambda binst_to_check, reg_to_check: binst_to_check.i == dual_id)
+
+
+handled_operations = {
+    ModPlus(): '"X"',
+    Circle(filled=True): '"•"',
+    Circle(filled=False): '"◦"',
+    LarrowTextBox(text='∧'): '"X"',
+    RarrowTextBox(text='∧'): '"X"',
+}
+
+
+def composite_bloq_to_quirk(
+    cbloq: CompositeBloq, line_manager: Optional[LineManager] = None, open_quirk: bool = False
+) -> str:
+    """Convert a CompositeBloq into a Quirk circuit URL."""
+    if line_manager is None:
+        line_manager = SparseLineManager(cbloq)
+
+    msd = get_musical_score_data(cbloq, manager=line_manager)
+
+    sparse_circuit = [(['1'] * (msd.max_y + 1)).copy() for _ in range(msd.max_x)]
+    for soq in msd.soqs:
+        try:
+            gate = handled_operations[soq.symb]
+            sparse_circuit[soq.rpos.seq_x][soq.rpos.y] = gate
+        except KeyError:
+            pass
+
+    empty_col = ['1'] * (msd.max_y + 1)
+    circuit = [col for col in sparse_circuit if col != empty_col]
+    if circuit == []:
+        raise ValueError(f"{cbloq} is an empty circuit")
+    # deleting lines of the circuit which are not used (happens with partition)
+    if circuit:
+        num_lines = len(circuit[0])
+        lines_to_keep = [i for i in range(num_lines) if any(col[i] != '1' for col in circuit)]
+        circuit = [[col[i] for i in lines_to_keep] for col in circuit]
+
+    quirk_url = "https://algassert.com/quirk"
+    start = '#circuit={"cols":['
+    end = ']}'
+    url = quirk_url + start + ','.join('[' + ','.join(col) + ']' for col in circuit) + end
+
+    if open_quirk:
+        subprocess.run(["firefox", url], check=False)
+
+    return url
+
+
+def bloq_to_quirk(
+    bloq: Bloq, line_manager: Optional[LineManager] = None, open_quirk: bool = False
+) -> str:
+    """Convert a Bloq into a Quirk circuit URL.
+
+    The input bloq is decomposed and flattened before conversion. Only a limited set
+    of operations is currently supported: control, anti-control, and NOT.
+
+    Args:
+        bloq: The bloq to export to Quirk.
+        line_manager: Line manager used to assign and order circuit lines.
+        open_quirk: If True, opens the generated URL in Firefox.
+
+    Returns:
+        A URL encoding the corresponding Quirk circuit.
+    """
+    try:
+        cbloq = bloq.decompose_bloq().flatten()
+    except DecomposeTypeError:  # no need to flatten the bloq if it is atomic
+        cbloq = bloq.as_composite_bloq()
+
+    return composite_bloq_to_quirk(cbloq, line_manager=line_manager, open_quirk=open_quirk)
diff --git a/qualtran/quirk_interop/bloq_to_quirk_test.py b/qualtran/quirk_interop/bloq_to_quirk_test.py
new file mode 100644
index 000000000..9f6dde4d8
--- /dev/null
+++ b/qualtran/quirk_interop/bloq_to_quirk_test.py
@@ -0,0 +1,64 @@
+import pytest
+
+from qualtran import BloqBuilder, QAny
+from qualtran.bloqs.basic_gates import Toffoli, XGate
+from qualtran.bloqs.bookkeeping import Allocate, Join, Split
+from qualtran.quirk_interop.bloq_to_quirk import (
+    SparseLineManager,
+    bloq_to_quirk,
+    composite_bloq_to_quirk,
+)
+
+
+def _build_split_join_split_cbloq(n):
+    bb = BloqBuilder()
+    q1 = bb.add(Allocate(QAny(n)))
+    q2 = bb.add(Allocate(QAny(n)))
+    qs1 = bb.add(Split(QAny(n)), reg=q1)
+    qs2 = bb.add(Split(QAny(n)), reg=q2)
+    for i in range(n):
+        qs1[i] = bb.add(XGate(), q=qs1[i])
+    q1 = bb.add(Join(QAny(n)), reg=qs1)
+    q2 = bb.add(Join(QAny(n)), reg=qs2)
+    qs1 = bb.add(Split(QAny(n)), reg=q1)
+    qs2 = bb.add(Split(QAny(n)), reg=q2)
+    for i in range(n):
+        qs2[i] = bb.add(XGate(), q=qs2[i])
+    q2 = bb.add(Join(QAny(n)), reg=qs2)
+    q1 = bb.add(Join(QAny(n)), reg=qs1)
+    return bb.finalize(q1=q1, q2=q2)
+
+
+@pytest.mark.parametrize("n", range(3, 6))
+def test_sparse_line_manager_builds_dual_maps(n):
+    cbloq = _build_split_join_split_cbloq(n)
+    manager = SparseLineManager(cbloq)
+
+    assert manager._join_to_split_id
+    assert manager._split_to_join_id
+
+
+@pytest.mark.parametrize("n", range(3, 6))
+def test_composite_bloq_to_quirk_url_shape(n):
+    cbloq = _build_split_join_split_cbloq(n)
+    url = composite_bloq_to_quirk(cbloq)
+
+    assert url.startswith('https://algassert.com/quirk#circuit={"cols":[')
+    assert url.endswith(']}')
+
+
+def test_composite_bloq_to_quirk():
+    cbloq1 = _build_split_join_split_cbloq(1)
+    url1 = composite_bloq_to_quirk(cbloq1)
+    assert url1 == 'https://algassert.com/quirk#circuit={"cols":[["X",1],[1,"X"]]}'
+    cbloq2 = _build_split_join_split_cbloq(2)
+    url2 = composite_bloq_to_quirk(cbloq2)
+    assert (
+        url2
+        == 'https://algassert.com/quirk#circuit={"cols":[["X",1,1,1],[1,"X",1,1],[1,1,"X",1],[1,1,1,"X"]]}'
+    )
+
+
+def test_bloq_to_quirk_on_atomic():
+    url = bloq_to_quirk(Toffoli())
+    assert url == 'https://algassert.com/quirk#circuit={"cols":[["•","•","X"]]}'