Every number in this atlas is computed against a pinned literature version. This page is the reading guide and the authority map: what each paper contributes, which parts the engine implements, and where the boundary of our claims sits.
| # | Reference | Read for |
|---|---|---|
| ① | Coecke & Kissinger, Picturing Quantum Processes, ch. 2–3 | string diagrams, ZX syntax & semantics intuition (foundation, not the whole book) |
| ② | Kissinger & van de Wetering, Picturing Quantum Software (zxcalc/book) | circuit optimization with PyZX — read while running |
| ③ | RPK24 v4 · arXiv:2410.17240 (2026-07-21) | the constitution: ZX distance (Def 3.1), distance-preserving rewrites, Prop 3.3, Floquetification — read closely |
| ④ | RPK25 · arXiv:2506.17181, Fault Tolerance by Construction | fault equivalence, fault gadgets, constructive fault tolerance — read their next move |
| ⑤ | Rüsch 2025 · arXiv:2510.08477 (+ fault-gadgets repo) | completeness for fault equivalence of Clifford ZX diagrams, engineering practice |
| ⑥ | arXiv:2603.19522 · MWPM-decodability in fault-equivalent rewrites | track only — overlap check due in M0; we do not compete with this direction |
Problem. High-weight stabilizer measurements are the bottleneck of fault-tolerant QEC: they spread correlated errors and resist hardware implementation. RPK24 turns any stabilizer code into a Floquet code using only single- and two-qubit operations, with distance and number of logicals provably preserved; overhead is linear in the maximum measurement weight of the original code.
What the atlas takes from it. The very concept we map: ordinary ZX rewriting preserves linear-map equivalence but generically breaks code distance, because a rewrite can spread a weight-3 Pauli error into a weight-5 one. RPK24 defines distance-preserving rewrite as the refined equivalence that forbids harmful error-propagation paths. Our engine implements Def 3.1 (ZX distance under postselected measurement semantics) and uses Prop 3.3 as a free oracle: the ZX distance of a code's establishment circuit equals d, with zero rewriting applied.
Reported Floquetification experiments (from the paper):
| Code | Original | Decomposed | Distance kept | Ancillas |
|---|---|---|---|---|
| 3-qubit repetition | [[3,1,1]] | [[3,1,1]] | yes | 0 |
| 5-qubit perfect | [[5,1,3]] | [[9,1,3]] | yes | 4 |
| 6-qubit | [[6,2,2]] | [[9,·,2]] | partial* | 3 |
| 4-qubit | [[4,2,2]] | [[4,2,2]] | yes | 0 |
*partial rows in early implementations trace to coarse ancilla management; the full algorithm in the paper resolves them via finer scheduling. The atlas engine does not rely on this table — it recomputes distances from scratch.
Why the rewrite space needs mapping. RPK24 exhibits a constructive path (high-weight → low-weight) inside the distance-preserving fragment. The atlas asks the complementary question: across the whole sampled rewrite space, where does distance actually break, and which structural neighborhoods never break? Map first, then navigate.
Core objects. Fault equivalence: circuit C₁ ≈ C₂ when every undetectable fault in C₁ has a counterpart in C₂ of no greater weight — a preorder on circuits, not a plain equivalence. Fault gadgets: diagram constructions that split a ZX diagram into a fault-free part plus enumerated Pauli noise on every wire, tensor-compatible and composition-preserving by design.
What the atlas takes from it. Two transfer lessons. First, the weight bookkeeping discipline: any atlas claim about Δd is a statement about minimal fault weights, so every rule card carries denominators and weight histograms. Second, the gadget view of noise: when the engine's Path A enumerates Pauli errors on a ZX diagram, it is effectively working in the gadget-annotated fragment — this keeps Path A and Path B (stabilizer-side min-weight N(S)∖S) on comparable footing.
Where the boundary sits. RPK25's extraction step (ZX → physical circuit) preserves fault equivalence but is not faithful: distinct diagrams can extract to the same circuit. The atlas deliberately stays on the diagram side — its nodes are canonical ZX graphs, and physical-circuit questions are out of scope for v1.
Core result. A finite rewrite rule set that is sound and complete for fault equivalence of Clifford ZX diagrams, via a unique normal form: every Clifford ZX diagram with noise annotations reduces to a canonical representative, and diagrams are fault-equivalent iff they share the normal form. Soundness means derivable ⇒ semantically fault-equivalent; completeness means semantically fault-equivalent ⇒ derivable.
What the atlas takes from it. The normal-form existence is precisely why our T0 canonicalization is well-posed: node identity in the rewrite graph is computed via a canonical form, and the literature guarantees such forms exist in the Clifford fragment the engine starts in. The atlas does not need the full rule set — it needs the distance profile of the basic rules — but completeness tells us the map is drawn in a territory where "same distance, same graph" questions are decidable to ask.
Honesty note. Completeness is Clifford-only; non-Clifford fault-equivalence completeness is open. City boundaries (d=3 Clifford regime) are chosen to stay inside the fragment where these guarantees exist.
Neighboring direction: which fault-equivalent rewrites preserve MWPM decodability. The atlas does not enter this lane — we compute distances and chart breakage, we do not certify decoders. Overlap confirmation is an M0 checklist item; the two projects are complementary, not competing.