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Urgent backfill: pinpoint corrections and 19 overlooked papers - #398

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Oct 13, 2026
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Pinpoint corrections and citations for the 19 most urgent missing papers (U1 in the arXiv backlog triage), plus the bb5 correction. Each change was checked against the paper's LaTeX. No new entries and no relation changes.

Corrections to current statements

  • classical_into_quantum: lower and upper bound on the cq error exponent were swapped. Dalai (1201.5411) is the upper bound. The lower bound is co-cited with Renes (2407.11118), who proved it independently of Li-Yang (2407.12403).
  • approximate_qecc: the Bény-Oreshkov condition paired (\Pi E_i^\dagger E_j \Pi) with (|i\rangle\langle j|), which is the transpose. Now (\Pi E_j^\dagger E_i \Pi), as corrected in 2607.22995 (a misprint inherited from 0907.5391 Cor. 2). You are a co-author of 2607.22995.
  • multimodegkp: the cubic phase gate is unsuitable only for unbiased GKP states. With on-demand noise biasing, its logical error vanishes with squeezing (2511.20355).
  • bacon_shor: stabilizers can be measured directly and fault tolerantly with one bare ancilla (1804.01127). The existing sentence and its citations are kept.
  • topological: 1311.0019 was not the sole "first" non-Abelian error-correction study. 1310.3846 is concurrent, with an earlier v1.
  • qubits_into_qubits: Clifford+T universality cited Barenco et al. (quant-ph/9503016), which proves CNOT plus arbitrary single-qubit gates. It now cites Boykin et al. (quant-ph/9906054) in both places. The threshold item misattributed the optimal-transport bound to Razborov. It now gives Razborov's (1/2) bound and points to 2309.16241 for local update recovery.
  • qubit_stabilizer: the bipartition identity (g(M)+g(M^\perp)=2k) now cites Yoshida-Chuang (1002.0085, Thm. 1).
  • 3d_surface: Kim's model (1012.0859) is not equivalent to copies of the 3D surface code. It is a 3D XYZ color code realizing one copy of the 3D fermionic surface code phase (2509.18324).
  • surface: the (O(d))-rounds sentence is qualified for transversal Clifford circuits with correlated decoding (2406.17653).
  • bb5: "improve the best-known BB6 distances" was false under the Zoo's BBw naming. The comparison is now restricted to BB6 codes of the 2308.07915 form, as in 2503.22071. A weight-6 BB code [[30,4,6]] already exists in the cited 2408.10001 (verified by brute force: k=4, d=6).
  • quantum_convolutional: quant-ph/0304189 finds the most likely error, not the most likely class. The degenerate Viterbi decoder (1204.2439) is added.

Overlooked foundational papers

  • qubit_stabilizer rate: degenerate codes beat the hashing bound (quant-ph/9604006, quant-ph/9706061; f > 0.80944 vs 0.81071).
  • qubit_stabilizer fault tolerance: flag error correction for any stabilizer code with d+1 extra qubits (1912.09549).
  • surface and toric: original Markov-chain Monte Carlo decoder, 18.5% (1202.4316).
  • surface and rotated_surface: BP-weighted MWPM, 17.76% (1709.02154).
  • qldpc fault tolerance: constant rounds per operation for transversal Clifford circuits (2406.17653).
  • tetrahedral_color introduced: Bombin and Martin-Delgado's tetrahedral 3-colexes with transversal (T) (quant-ph/0610024).
  • color, 488_color and 3d_color: restriction decoder, at 10.2% (4.8.8) and 0.77% / 13.1% (bcc) (1905.07393).
  • gkp encoders: heralded single-qubit preparation (quant-ph/0205114).
  • cat: the general multi-component construction is now cited (1605.00357).
  • qudit_surface: first RG decoder for (\mathbb{Z}_d) surface codes, with threshold 13% for (\mathbb{Z}_3) (1302.3638).
  • quantum_double_dihedral: about 7% for the (S_3) charge submodel (1310.3846).

Deliberately left out

  • New entries from 2509.18324 (chiral color code family, 3D XYZ color code) and the error-set AQEC model of 2607.22995. These are larger additions for a separate PR.
  • The Bacon-Shor-13 vs Surface-17 comparison in 1804.01127 (a paper-internal comparison).
  • A caveat on the >1% surface-code threshold of 1009.3686. Only a footnote in 2101.02211 states that it was not reproduced, and the existing 0.5–2.9% range stays true.
  • dlv, approximate_qecc (quant-ph/0004088) and gross were checked against their revised arXiv versions. No change is needed.

Overlap: PR #396 also edits toric and topological, in different lines. Whichever merges second will need a one-line changelog conflict resolved.

🤖 Generated with Claude Code

Corrections: classical_into_quantum (cq error-exponent bounds swapped),
approximate_qecc (Beny-Oreshkov index order), multimodegkp (cubic phase gate
with noise biasing), bacon_shor (direct stabilizer measurement), topological
(concurrent first non-Abelian decoders), qubits_into_qubits (Boykin et al. for
Clifford+T; Razborov bound), qubit_stabilizer (Yoshida-Chuang bipartition),
3d_surface (Kim's model is a 3D XYZ color code), surface (O(d) rounds
qualified), bb5 (BB6 comparison scoped), quantum_convolutional (degenerate
Viterbi).

Citations: quant-ph/9604006, quant-ph/9706061, 1912.09549, 1202.4316,
1709.02154, 2406.17653, quant-ph/0610024, 1905.07393, quant-ph/0205114,
1605.00357, 1302.3638, 1310.3846.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

Related models \cite{arxiv:cond-mat/0607736,arxiv:1012.0859} on lattices with certain colorability are equivalent to several copies of the 3D surface code \cite{arxiv:1908.08049}.
Related models \cite{arxiv:cond-mat/0607736} on lattices with certain colorability are equivalent to several copies of the 3D surface code \cite{arxiv:1908.08049}.
The non-CSS model of Ref. \cite{arxiv:1012.0859} is instead a version of the 3D XYZ color code, which realizes a single copy of the \hyperref[code:3d_fermionic_surface]{3D fermionic surface code} phase \cite{arxiv:2509.18324}.

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Shouldn't this be on xyz color entry instead?

Tamara and others added 3 commits October 13, 2026 05:55
…review 5501715020)

The sentence on Kim's non-CSS model (arXiv:1012.0859) and the fermionic
surface code phase concerns the 3D XYZ color code of arXiv:2509.18324,
not the 3D surface code. It now sits in xyz_color as a 3D-version
paragraph, with a cousin to 3d_fermionic_surface.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
…5020)

Per the zookeeper, the 3D XYZ color code of arXiv:2509.18324 gets its own
entry (parents qldpc, 3d_stabilizer; cousins xyz_color,
3d_fermionic_surface, 3d_color, 3d_subsystem_color), with Kim's model
(arXiv:1012.0859) in its description. xyz_color returns to its main-branch
state; the cousin is declared on 3d_xyz_color only.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
…24 and 1012.0859

3d_xyz_color: spell out the color-to-Pauli face rule and why generators
commute; name the bitruncated cubic honeycomb for Kim's model; mention
the qudit chiral color code; cite Kim for k=b_2; add the [[15,1,3]]
tetrahedral instance and the single-shot fault-tolerance item; cite and
reword the xyz_color and 3d_subsystem_color cousin details.
3d_surface: drop the redundant 2026-10-13 changelog item.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Tamara and others added 3 commits October 13, 2026 09:49
list_color: add 3d_xyz_color through a manual_code_list selector (the
predicate name the site build's schema accepts), leaving the hierarchy
without a color parent, as decided by the zookeeper.
3d_xyz_color: add topological_abelian as a secondary parent (it realizes
the Abelian fermionic toric code phase, as do 3d_color and
3d_fermionic_surface) and a single_shot cousin (single-shot via gauge
fixing, arXiv:2509.18324 Sec. 3.3), which place it in the topological
and single-shot lists.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
…wist-defect taxonomy)

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
Conflicts only in the _meta changelogs of topological.yml and toric.yml:
kept both entries, newest first ('2026-10-12' from this PR, then
'2026-10-11' from #396). #396's toric -> qcga parent and topological
rate sentence and #398's backfill edits both survive unchanged.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
@valbert4
valbert4 merged commit b7f3e69 into main Oct 13, 2026
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