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Distributed Proof Theory and Quantum Algorithm Verification

Jincheng Zhang

Published Sep 5, 2026• 0 citations
Publisher

Abstract

This paper explores the convergence of Distributed Proof Theory (DPT) with quantum computing, proposing a novel methodology for algorithm verification. DPT offers a formal, model-independent approach to verifying algorithms through the construction of distributed proofs. The core idea is to augment this process with quantum algorithms, specifically amplitude estimation, to achieve exponential speedups in the verification process. We detail the theoretical framework, emphasizing the utilization of quantum parallelism to efficiently handle the complex relationships within distributed proofs. The proposed system represents a significant advancement in algorithm assurance, potentially revolutionizing the landscape of software and hardware verification. The central equation illustrating the verification process is: $P(correct) = |Amplitude(correct)|^2$, where $P(correct)$ represents the probability of the algorithm being correct, and $Amplitude(correct)$ is the quantum amplitude calculated by the amplitude estimation algorithm. The key step involves transforming the distributed proof into a quantum state, and then employing amplitude estimation to determine the probability of that state representing a correct proof. This approach dramatically reduces the computational complexity compared to traditional verification techniques.

DOI
10.5281/zenodo.22332515

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