把 surface 与 Bacon–Shor subsystem 结构映射到低度 heavy-hex 图，并用 flag qubits 恢复完整码距的硬件感知码族。
聚焦码构造与受限连接性；具体芯片、控制栈和实验结果属于 hardware/experiment 领域。
code/hardware-aware/heavy-hexCode dossier
这里汇总参数景观中的结构化记录、码族谱系中的构造说明、执行路线与外部知识库，作为完整主题页的代码专属延伸。
原论文给出 [[d²,1,d]] 数据码块；本点取 d=3。n 不含 flag/measurement ancillas，检查权重按直接 gauge 测量而非稳定子乘积。
原论文给出 [[d²,1,d]] 数据码块；本点取 d=3。n 不含 flag/measurement ancillas，检查权重按直接 gauge 测量而非稳定子乘积。
d² data-qubit heavy-hexagon subsystem patch；只计直接测量 gauge checks
heavy-hex connectivity
flag-assisted checks
matching adaptation
聚焦码构造与受限连接性；具体芯片、控制栈和实验结果属于 hardware/experiment 领域。
Heavy-hexagon d=3 [[9,1,3]] Execution Route：低度连接图、flag/gauge 测量、稳定子推断与硬件约束解码。当前路线绑定 Flag-aware lookup、Heavy-hex graph decoder，并覆盖 Flag-assisted gauge extraction、Repeated subsystem syndrome。
散点 n 只计 data qubits；完整硬件 footprint 必须另加 ancillas。
同名构造与有限硬件实例必须分开；精确比较需匹配布局、边界、flag 调度、校准噪声和联合解码。
2020Topological and Subsystem Codes on Low-Degree Graphs with Flag QubitsDeep reference
定义、代数构造、保护能力与执行证据均按来源段落独立维护；中文稿经过术语整理，英文稿保留用于逐段对照。
Heavy-hex 码是面向低度 heavy-hexagon 超导连接图的子系统/混合检查方案，目标是在有限连接和串扰约束下实现距离保护。其 X 与 Z 检查采用不对称的 Bacon–Shor 型与表面码型结构，并用旗标处理故障传播。
The heavy-hex code is a subsystem or hybrid-check construction tailored to low-degree heavy-hexagon superconducting connectivity. Its asymmetric Bacon-Shor-like and surface-code-like X/Z structures use flag information to manage fault propagation under connectivity and crosstalk constraints.
数据量子比特置于 heavy-hex 图，低权重 gauge 测量经乘积形成目标稳定子；部分高权重检查通过 flag ancilla 分解。实例必须保存布局、数据/测量/旗标角色、CNOT 次序和边界，而不只是抽象稳定子矩阵。
Data qubits occupy a heavy-hex graph, with low-weight gauge measurements multiplied into target stabilizers and some higher-weight checks decomposed using flag ancillas. An instance must store layout, data/measure/flag roles, CNOT order, and boundaries, not only an abstract stabilizer matrix.
距离由给定边界中最短逻辑 Pauli 决定，但线路中的 hook error 可能降低有效距离。旗标结果用于识别会模仿低权重综合征的危险传播，因此保护声明必须同时覆盖数据误差和电路故障。
Distance is set by the shortest logical Pauli for the chosen boundaries, while circuit hook errors may reduce effective distance. Flag outcomes identify dangerous propagation that can mimic low-weight syndromes, so protection claims must cover both data errors and circuit faults.
距离 d 的有限实例量子比特数和检查数由 heavy-hex 布局与边界约定决定，不能直接套用旋转表面码的 d² 公式。资源表应分列数据、综合征 ancilla、flag ancilla、测量深度和最大并发度。
Qubit and check counts for distance d depend on the heavy-hex layout and boundary convention and should not reuse the rotated-surface d-squared formula. Resource tables should separate data, syndrome ancillas, flag ancillas, measurement depth, and maximum concurrency.
主要逻辑操作依赖 Pauli frame、边界变形、码块拼接或注入资源，而不是物理逐比特通用横向门。heavy-hex 连接约束会改变 lattice surgery 和逻辑测量的调度成本。
Logical operations primarily use Pauli frames, boundary deformation, block surgery, or injected resources rather than a universal qubitwise transversal set. Heavy-hex connectivity changes the scheduling cost of lattice surgery and logical measurements.
解码输入应同时包含稳定子综合征、gauge 结果、flag 触发和多轮时间信息。可在带 flag 条件权重的匹配图或最大似然模型上推断；忽略 flag 会把电路信息丢成普通码容量问题。
Decoder input should include stabilizer syndromes, gauge outcomes, flag triggers, and multiple rounds. Inference can use a matching graph or likelihood model conditioned on flags; ignoring flags collapses circuit information into an inappropriate code-capacity problem.
检查分解与门次序按单故障可诊断性设计，但阈值或伪阈值仍依赖具体门噪声、读出、复位和串扰模型。低连接度是硬件约束优势，不自动等于更高逻辑阈值。
Check decomposition and gate order are designed for single-fault diagnosability, but thresholds and pseudothresholds still depend on gate, readout, reset, and crosstalk noise. Low connectivity is a hardware advantage, not an automatic logical-threshold advantage.
该构造直接针对 heavy-hex 超导芯片，可减少不在耦合图上的 SWAP 和并行冲突。实验映射必须核对真实芯片子图、禁用耦合边、校准快照及 flag 处理。
The construction directly targets heavy-hex superconducting chips, reducing off-graph SWAPs and parallel conflicts. Experimental mapping must verify the actual chip subgraph, disabled couplers, calibration snapshot, and flag processing.
Heavy-hex 码借鉴 Bacon–Shor 子系统测量和表面码拓扑边界，但不是任意 heavy-hex 图上的表面码同义词。与标准 surface/compass 码的关系应通过 gauge、稳定子中心和边界逐项说明。
The heavy-hex code borrows subsystem measurements from Bacon-Shor and topological boundaries from surface codes, but it is not synonymous with any surface code drawn on a heavy-hex graph. Relations to surface and compass codes require explicit gauge, stabilizer-center, and boundary comparisons.
名称同时指构造思想与若干有限硬件实例。精确外链需要匹配距离、布局版本、量子比特角色、检查调度和解码器；仅有 [[n,k,d]] 或“heavy hex”标签只能算候选。
The name denotes both a construction idea and several finite hardware instances. An exact external link must match distance, layout version, qubit roles, check schedule, and decoder; [[n,k,d]] or a “heavy hex” label alone is only a candidate.