research
A Fault Threshold Reaches Non-Abelian Memory
An explicit syndrome circuit and online decoder extend provable circuit-level protection to every two-dimensional non-chiral topological order.
Summary
An explicit syndrome circuit and online decoder extend provable circuit-level protection to every two-dimensional non-chiral topological order.
Fault-tolerance proofs are strongest when they cover the complete circuit, including noisy syndrome extraction, rather than an idealized decoder alone. This work constructs syndrome-extraction circuits from the Turaev-Viro path integral and pairs them with a classical algorithm that decodes as measurements arrive. Under a local stochastic circuit-level noise model, the authors prove a threshold for quantum memory in any two-dimensional non-chiral topological order, including non-abelian phases, and outline how the construction can support topological logical gates. It is a mathematical scheme and threshold proof, not a fabricated memory or an experimental error rate, but it closes a generality gap between exotic topological phases and explicit fault-tolerant circuitry.
Why it matters
An explicit syndrome circuit and online decoder extend provable circuit-level protection to every two-dimensional non-chiral topological order.
Limits and context
- It is a mathematical scheme and threshold proof, not a fabricated memory or an experimental error rate, but it closes a generality gap between exotic topological phases and explicit fault-tolerant circuitry.
Key claims
An explicit syndrome circuit and online decoder extend provable circuit-level protection to every two-dimensional non-chiral topological order.
Qualification: It is a mathematical scheme and threshold proof, not a fabricated memory or an experimental error rate, but it closes a generality gap between exotic topological phases and explicit fault-tolerant circuitry.
Evidence: source-2026-11-08-001
Sources
- arXiv preprint 2611.08488, original v1arXiv · primary research
Corrections
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