Colour code (transversal Cliffords) code_color

A 2D topological stabiliser code on a three-colourable trivalent lattice, each plaquette carrying an X and a Z stabiliser of weight 6. Because the two types share support, the entire Clifford group — H, S, CNOT — is transversal, where the surface code gets only CNOT natively and pays lattice surgery for the rest. Bombín and Martín-Delgado introduced it in 2006 D[663]; the first full hardware demonstration is Google's, submitted December 2024 D[41]. The price is density: ~1.9× the surface code's teraquop footprint, 1,250 against 650 physical per logical at 0.1% noise S[655]fact.
d = static triangular lattice, no transport; e = inherits the host's control modality and placement [graph].
f = Pauli stabilisers only; a = 0.5 — identical on fabricated and natural carriers, needing only a static nearest-neighbour lattice [graph].

The transversal gate needs no merge/split: Google puts a logical Hadamard at ~20 ns against ~1,000× longer through lattice surgery C[664]. Weight-6 checks mean deeper extraction and hook errors that cut the effective distance unless the schedule avoids them — a 2026 construction avoids all malign bulk hook errors with one auxiliary per plaquette S[665]. Errors also fire three detectors, so the syndrome is a hypergraph: matching does not apply and decoders must project or search. Hence the gap: Λ₃/₅ = 1.56(4) D[41] against 2.14 for the surface code on the same processor family D[1], and Google's 2026 d=5 colour-code memory reached 8.19(14)×10⁻³ per cycle only with the search-based Tesseract decoder D[2]. What moves the floor is circuit scheduling and decoders, not the code.

Dominant term: the syndrome round, not the transversal gate — weight-6 extraction and hypergraph decoding leave Λ at 1.56 against 2.14 D[1], [41].

No fabrication of its own: it inherits the host's chip, trap or tweezer array, tiled hexagonally rather than square, and brings no new supplier D[41]. Export exposure is the host's: ECCN 4A906 (BIS, 2024-09-06) controls a quantum computer only when its qubit count and C-NOT error fall in the same band — from 34–99 qubits at ≤ 10⁻⁴ to any error from 2,000 qubits on fact — while the code is published mathematics from 2006 D[663].

Control and readout per qubit match the host's surface-code burden. The difference is per round: each data qubit sits in six weight-6 checks against the surface code's four weight-4 checks, so a round costs about 1.5× the two-qubit gates on a deeper schedule, and that is where the threshold goes. Against it, a logical Clifford needs no merge/split rounds at all. Decoding is the harder item: hypergraph syndromes rule out a stock matching engine, and the only published d=5 hardware decode is Google's Tesseract search decoder D[2].

Sits, as an alternate code, in four architectures — the transmon lattice with tunable couplers, trapped-ion QCCD, the linear Paul trap with individual laser addressing and the alkali Rydberg tweezer array [graph]; requires the same static nearest-neighbour lattice as the surface code and hosts magic-state factories. All three 2025–26 magic-state milestones ran in colour codes: cultivation to 0.9999(1) at 8% acceptance before code-switching out D[42], Quantinuum's [[15,1,3]]→[[7,1,3]] switching at ≤5.1(2.7)×10⁻⁴ D[666], QuEra's 5-to-1 distillation D[147]. It replaces the surface code where transversal Cliffords beat the ~1.9× footprint; switching costs a decoder and a layout, not hardware. Clock contribution ~20 ns per logical Hadamard C[664]; the code does set d₂, the gate-layer count summed into the round (derived clock = sum of the syndrome round: gate layers + transport + readout + reset for the architecture), 0.65 µs derived against the measured 1.1 µs host cycle. Neighbouring empty slot: no hardware colour-code decoder.

Λ₃/₅ = 1.56(4) and the 0.0027(3) transversal-Clifford error are Google's own, one processor, unreplicated by a second vendor D[41]. Two framings of that paper conflict: it reports 86.5(1)–90.7(1)% teleported-state fidelities for lattice surgery, while Google's blog presents 86–91% as "two-qubit gate fidelity" C[664] — trust the paper. Magic injection exceeds 99% only with post-selection keeping ~75% of runs D[41]. The footprint claims are not comparable either: "fewer physical qubits per code distance" C[664] against total qubits for a fixed logical target S[655]. Nothing published separates code error from decoder error in the transversal figure.

Not published: a quantified Monte Carlo improvement for the hook-error-free colour-code circuit [665].

Who.
| Organisation | Role | Country | What they do | Evidence |
|---|---|---|---|---|
| Google Quantum AI | Developer/user | US | Only superconducting colour-code memory; cultivation host | D[41], [42] |
| Quantinuum | Developer/user | US | Colour-code code switching; tesseract [[16,6,4]] on Helios | D[666], [667] |
| Microsoft Quantum | Developer | US | Co-authored the tesseract colour-code result | D[667] |
| QuEra | Developer/user | US | First logical 5-to-1 distillation on colour-code patches | D[147] |

Money. 2025-07-14 · QuEra · publication (first logical 5-to-1 distillation) · no figure · funded from its $230 M+ 2025 round C[153] · published D[147]. 2025-11-06 · DARPA QBI Stage B · up to $15 M per team · eleven teams, Quantinuum and QuEra among them G[65]. 2026-06-03 · Quantinuum · IPO · $1.68 B gross at $60/share, Nasdaq QNT; Q2-2026 revenue $8.0 M, cash $2.1 B · closed G[123]. No round, grant or acquisition is specific to the colour code: it is a line item inside platform programmes.

Market & supply chain. No dedicated supply chain; it rides the host's fab and the general classical stack. The market it moves is decoding: hypergraph syndromes need search or projection decoders (FPGA/GPU work from AMD and NVIDIA), and no vendor ships a colour-code hardware decoder as of 4 Sep 2026. Pays into G3 and G4 through magic-state factories: every logical magic-state milestone since 2025 ran in a colour code D[42], [147], [666].

IP & standards. The code is published mathematics from 2006 D[663]. PatSnap's April 2026 landscape counts 12 QEC patents — Google 6, IBM 4, Tencent 2 — with no colour-code cluster P[668]. Google's granted surface-code patent covers gauge operators, not this code fact. No standards body; the de facto interface is a Stim detector-error model.

Roadmaps & track record. Google (2025-06-23 · colour code a "workhorse configuration", no dated milestone · a d=5 memory followed in July 2026) C[664]D[2]. Quantinuum (2024-09 · Helios 2025 → Sol 2027 → Apollo 2029 · Helios shipped 2025-11-05 and carried the tesseract result) Rfact. QuEra (2026-06 · Libra, >256 logical, 2028 · its January-2024 roadmap promised 100 logical in 2026, undelivered) Rfact. Google's claims have been measurements, not promises; Quantinuum's schedule has held; QuEra's research runs ahead of its product roadmap.

Strategic reading. The colour code favours platforms where qubits are cheap and logical time expensive — superconducting and neutral atoms — over trapped ions, where a 1.9× premium falls on the scarce resource. Its likeliest 2029 position is not memory but the T-state factory feeding surface-code memory: cultivation cut magic-state cost ~40× inside a colour code and then switched out D[42], making it a component of a surface-code machine rather than a competitor. Substitution threats: high-rate qLDPC blocks with transversal gates, and algorithmic fault tolerance replacing O(d) rounds per logical gate. Losers: toolchains built only around lattice surgery.

Confirm/demote in 12–24 months: a colour-code memory beyond d=5 with Λ approaching 2.14; a second vendor reproducing transversal Cliffords. Best case 2029: cultivation makes it the standard magic-state substrate, the footprint premium confined to factory patches. Worst case: hook-error and decoder overheads keep Λ near 1.5 and it survives only as a distillation substrate. Open questions: does the one-auxiliary-per-plaquette circuit S[665] recover a competitive threshold on hardware; do planar non-Clifford circuits S[669] beat distillation; will anyone publish a total-footprint comparison.