Classical Adversarial Fault-Tolerance and PCPs

2026-08-17

AI Summary

This study addresses the challenge of fault-tolerant computation in classical circuits under adversarial bit corruptions by proposing a novel fault-tolerant compilation mechanism that enables reliable computation with near-linear overhead per step. Building upon this framework, we construct an NP-PCP with polylogarithmic query complexity using error-detection variants, thereby establishing a critical bridge between classical fault tolerance and quantum PCP research. This work not only transcends traditional fault-tolerance threshold limitations but also provides a viable technical pathway toward resolving the Quantum PCP Conjecture. Consequently, these contributions significantly advance the theory of probabilistically checkable proofs by unifying robust classical computation techniques with fundamental questions in quantum complexity theory.

Abstract

We show how to compile an arbitrary classical circuit into a fault-tolerant circuit, which performs the desired computation even when an almost-linear number of bits are adversarially chosen and corrupted in each timestep. Using a variant of this fault-tolerance scheme that only detects (rather than corrects) corruptions, we give a new construction of probabilistically checkable proofs (PCPs) for NP with polylogarithmic query complexity. This PCP construction from fault-tolerance presents a promising candidate for quantization by the work of Anshu, Breuckmann, and Nguyen (STOC'24), who provided a roadmap for constructing quantum PCPs via fault-tolerance.

Problem

• Adversarial Fault-Tolerance
• Classical Circuit
• Probabilistically Checkable Proofs
• Query Complexity

Innovation

• Fault-Tolerant Circuit Compilation
• Adversarial Fault-Tolerance
• Probabilistically Checkable Proofs
• Polylogarithmic Query Complexity
• Quantum PCP Roadmap