“Decoded by matching” is incomplete. The graph, weights, correlation approximation, circuit, and noise normalization determine the actual decoder experiment.
Gidney, Newman, Fowler, and Broughton derive two interleaved spacetime matching graphs for the honeycomb memory. Detector events are vertices. Single modeled faults connect the detectors they can trigger, and edge weights come from the circuit-level fault probabilities. Correlation-aware minimum-weight perfect matching then chooses a likely fault class consistent with the observed boundary.
The paper reports threshold ranges of approximately:
0.2%--0.3% for its six-step CNOT-based parity circuit;1.5%--2.0% for its native entangling-measurement model.These are literature claims under the paper's respective noise normalizations. They are not recomputed by constructor.py, and the difference between the ranges is evidence that “Honeycomb threshold” is not a well-defined phrase without the circuit model.
Benchmarking the Planar Honeycomb Code separates SD6, SI1000, and EM3 circuit assumptions. They differ in native operations, error locations, and normalization. Opening the torus also adds spatial boundary nodes and changes which fault chains are logically nontrivial.
Consequently, a fair comparison must hold fixed:
Paetznick et al. construct explicit Majorana parity-measurement circuits and their detector models. Poisoning and correlated parity faults do not map term-for-term onto depolarizing two-qubit-gate noise. The hardware motivation—native weight-two parity—is therefore also a warning against importing a superconducting threshold.
The X3Z3 variant changes the Pauli pattern to preserve bias. Its detector symmetry and matching simplifications belong to that variant, not to the unmodified Hastings-Haah schedule. Setiawan and McLauchlan also identify an obstruction to reducing the studied two-body dynamical class to one-dimensional decoding graphs. A favorable bias does not automatically make the original honeycomb graph one-dimensional.
A Dynamic Circuit for the Honeycomb Floquet Code changes physical roles during the cycle so measured/reset qubits remove leakage and timelike distance improves. Once the circuit changes, detector definitions and graph weights must be regenerated. “Same ideal edge measurements” does not imply “same fault-tolerant code.”
One physical fault may activate more than two detectors. A graph decoder either decomposes such correlations into weighted edges or supplements matching with correlation updates. Hypergraph or logical-class methods can retain different information. The 2026 worm-decoder work includes honeycomb Floquet examples by sampling logical-class probabilities, but this is a research decoder rather than a replacement for the registered standard MWPM row.
Before copying any threshold or logical-error rate, require all of:
If any item changes, the number is a new experiment. card.yaml therefore stores circuit-qualified decoder notes rather than a bare threshold field.