XZZX surface code

A rotated planar distance-d XZZX instance typically encodes one logical qubit in about d squared data qubits, with exact n and check counts set by boundary conventions. A threshold is not a code parameter and must include noise bias, measurement model, number of rounds, and decoder.

As for surface codes, deformation, lattice surgery, and Pauli-frame updates are the main logical-operation tools. Bulk local-Clifford equivalence does not produce a boundary- and bias-preserving universal transversal set; non-Clifford gates generally still use magic states or code switching.

The decoder should weight a spacetime graph consistent with XZZX checks and the biased channel, using weighted matching, tensor networks, or correlated inference. Mapping the code to CSS form is valid only if the noise channel is transformed at the same time.

Repeated syndrome rounds turn data and measurement faults into three-dimensional detection events, and CNOT order must keep hook errors away from the short logical direction. Bias-preserving extraction is part of the claim: gate noise that converts Z bias into X/Y faults can erase the predicted advantage.

XZZX is compatible with two-dimensional nearest-neighbor arrays and has resource geometry close to a rotated surface code. Hardware studies should report calibrated Pauli bias, leakage, correlations, and per-round detection events rather than substitute an ideal independent-Z simulation.

It is equivalent to the standard surface code under a suitable local Clifford transform but behaves differently in a fixed physical noise frame. Sharing a topological phase does not imply equal finite-size logical error rates; boundaries, schedules, and decoding weights control the comparison.

Do not quote a “high threshold” without its noise model: code-capacity, phenomenological, and circuit-level thresholds are different quantities. An external instance is exact only when lattice, boundaries, generators, bias direction, and syndrome rounds all match.