An unreviewed preprint posted to arXiv reports a method for compiling arbitrary classical circuits into fault-tolerant equivalents that remain correct even when an almost-linear number of bits per timestep are adversarially corrupted. The authors claim the construction handles a corruption budget that scales nearly with the total number of active bits—a substantially stronger adversarial model than many prior schemes.
A detection-only variant of the scheme yields what the authors describe as a new construction of probabilistically checkable proofs (PCPs) for NP with polylogarithmic query complexity. PCPs are a foundational object in complexity theory, encoding proofs so that a verifier can check correctness by reading only a tiny fraction of the proof; reducing query complexity while maintaining soundness is a long-standing goal. The paper does not itself establish a quantum PCP, but frames its classical fault-tolerance route as a natural candidate for quantization, citing a 2024 roadmap by Anshu, Breuckmann, and Nguyen (STOC'24) that outlined how quantum PCPs might be approached through fault-tolerant circuit compilation.
Because this is a preprint that has not yet undergone peer review, the claimed constructions and their parameters should be treated with appropriate caution until independent verification is complete. If the results hold, they would represent both a practical advance in classical fault-tolerance and a structural contribution to the ongoing effort to resolve the quantum PCP conjecture.