The Resonance Processing Unit (RPU) – Holonomic Hardware Geometries, Triorthogonal Codes, and the 1531-Anvil

Engineering notes

Key topics: autonomous driving. See the paper for implementation details and experimental results.

Chinese explanation / 中文解读

中文解读待补充：本站会优先为端到端自动驾驶、BEV感知、3D目标检测、轨迹预测、路径规划、LiDAR感知等高价值论文补充中文说明。

Original abstract

This working paper introduces the Resonance Processing Unit (RPU), a speculative quantum hardware architecture that proposes transitioning from active software-driven QEC to autonomous, Hamiltonian-driven fault tolerance. Rather than arranging qubits on 2D associative grids, the RPU conjectures that driving 7 standard superconducting transmons in the Fano-plane (PG(2,2)) incidence topology with an always-on G₂-invariant Hamiltonian can passively enforce error suppression via an engineered energy gap — an approach connected to the field of autonomous (passive) QEC. The paper defines two operational modes for the resulting 731-Core: a near-term mode running the established Steane [[7,1,3]] code natively in hardware (1 logical qubit, distance 3), and a speculative long-term mode targeting an 8-dimensional logical Quoct ([[7,3,d]]_O). The larger 1531-Anvil (PG(3,2), 15 resons) is proposed as the execution block for universal logic, with the conjecture that its incidence geometry may satisfy the triorthogonality conditions (Bravyi & Cross, 2015) required for transversal CCZ without Magic State Distillation. State transfer between the 2D memory and 3D execution block is proposed via unitary code deformation (Fibrational Boundary Injection), building on prior work by Bombín (2015) and Paetznick & Reichardt (2013). v18.2 integrates subsequent theoretical work that puts earlier conjectures on firmer ground. The Fano stabiliser group structure conjectured in earlier versions has been proved: the GHZ stabiliser group forms the seven lines of PG(2,2), with all stabiliser-line products equal to +I (doi:10.5281/zenodo.20516899, doi:10.5281/zenodo.21219698). The magic resource theory required to audit the 1531-Anvil's gate budget has been developed in full, with the total variation (TV) discriminant identifying the three-tier taxonomy of stabiliser, dark-magic, and genuine-magic states (doi:10.5281/zenodo.21219700). The Clifford/magic boundary has been given a cohomological characterisation: it is the non-trivial generator of H²(Sp(4,F₂);Z₂) ≅ Z₂, with the T gate as canonical representative (doi:10.5281/zenodo.21158943). Three concrete open questions remain as the critical path to validation: (1) formal construction of the always-on G₂ stabiliser Hamiltonian with computed energy gap; (2) proof that the PG(3,2) interpolation Hamiltonian is frustration-free; (3) verification that PG(3,2) satisfies the Bravyi–Cross triorthogonality conditions.

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