xzzx

Description

Non-CSS variant of the rotated surface code whose generators are XZZX Pauli strings associated, clockwise, to the vertices of each face of a two-dimensional lattice (with a qubit located at each vertex of the tessellation). \textit{XZZX…

Introduced in: arxiv:quant-ph/0205004, arxiv:1108.5490, arxiv:1201.3757, arxiv:2009.07851

Rationale

Re-scored 2026-05-23: XZZX is a parametric surface variant, so its distance proof remains homological (per the rotated-surface playbook), not by `decide` enumeration. But the new general non-CSS Pauli infrastructure -- `negIdentity_not_mem_of_indep_phase_zero_commute` (BinarySymplectic/SymplecticSpan.lean), `no_weight_two_mem_centralizer_of_anticommute_witness` (Core/CSSDistance.lean), and the `local instance` `Decidable (Anticommute p q)` template from FiveQubit_5_1_3 -- substantially reduces the witness-plumbing effort for the non-CSS pieces of the proof. Tractability bumped to 9 (homological with low-rank H^1, like rotated_surface but with Clifford-twisted plaquettes), effort bumped to 8. Previous rationale: XZZX surface code: a Clifford-twisted variant of the rotated surface code; non-CSS but generated by uniform XZZX plaquettes. Existing rotated-surface lattice and homological infrastructure should largely apply with a generator redefinition. Two hardware demos. Modest extension.

Scoring composite 8.25