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Quantumization of Zero-Knowledge Proofs and Verifiable Computation Circuits

Jincheng Zhang

Published Sep 1, 2026• 0 citations
Publisher

Abstract

This paper explores the quantumization of zero-knowledge proofs (ZKPs) and verifiable computation circuits (VCCs), presenting a novel approach to achieving secure and verifiable execution of quantum computation programs. The core idea involves leveraging quantum circuit hashing techniques to construct ZKP protocols that demonstrate the correctness of a VCC without revealing its underlying structure. This approach addresses a critical need within the burgeoning field of quantum computing – the provision of robust and trustworthy execution validation mechanisms. We outline the theoretical framework, detailing the key components of the system including the circuit hashing algorithm, the ZKP protocol design, and the associated mathematical formalization. The work contributes to the development of a new paradigm for quantum program verification, offering a potential pathway towards building more reliable and secure quantum computing systems. The presented methodology aims to bridge the gap between the theoretical promise of quantum computation and the practical challenges of ensuring its trustworthiness. ---

DOI
10.5281/zenodo.22226640

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Zero-knowledge proofs (ZKPs) enable the verification of a statement without revealing any information beyond its validity and constitute a fundamental primitive in cryptography and information theory. However, existing constructions rely on computational assumptions and are predominantly confined to bipartite settings, leaving their information-theoretic realization in bipartite or network scenarios largely unexplored. Here we develop a framework for zero-knowledge verification based on the indistinguishability of quantum states under operational constraints. Exploiting the fundamental limitations imposed by local operations, we show that a verifier is inherently restricted from extracting information about the underlying state while retaining the ability to verify correctness. We construct explicit protocols for multiparty quantum networks that achieve information-theoretic security, ensuring that no subset of collaborating parties can gain knowledge beyond the validity of the statement, independent of their joint computational power.
The verification of quantum circuits presents a significant challenge due to the exponential complexity associated with simulating quantum systems. Traditional methods are often computationally intractable for larger circuits. This paper proposes a novel approach to quantum circuit verification leveraging blockchain technology. The core idea is to create a decentralized, immutable record of quantum circuit executions. Each execution is represented as a transaction on the blockchain, incorporating circuit parameters, measurement results, and cryptographic hashes. Consensus mechanisms are employed to ensure the integrity and validity of the recorded data, mitigating the risk of manipulation or fraudulent results. This system offers a potential solution to the scalability issues inherent in current verification strategies and contributes to the broader field of quantum security and trust. The system aims to provide a verifiable audit trail for quantum computations, crucial for building confidence in quantum technologies.
Quantum circuit compilation is a crucial step in translating high-level quantum algorithms into executable quantum circuits on specific hardware. The complexity and potential for errors within this process necessitate rigorous verification methods. This paper proposes a novel approach leveraging symbolic execution to formally verify quantum circuit compilation. We represent quantum circuits and compilation steps as a symbolic program, enabling the exploration of all possible compilation paths. By incorporating quantum gate fidelities and noise models into the symbolic execution engine, we can identify potential errors in the compilation logic, providing a robust and systematic way to ensure the correctness of the compilation process. The core claim is that symbolic execution can be extended to formally verify the correctness of quantum circuit compilation processes. This work addresses a critical need in quantum computing, offering a new technique for building trust and reliability into quantum software.
This paper presents a novel approach to automated theorem proving specifically tailored for quantum circuit verification. The core idea is to construct a formal system that leverages logical reasoning and proof techniques to rigorously analyze quantum circuit designs. This system aims to identify errors and inconsistencies within the circuit, ensuring compliance with the fundamental principles of quantum mechanics. The proposed method moves beyond traditional circuit simulation, offering a mathematically sound guarantee of correctness. We detail the architecture of the theorem prover, focusing on the representation of quantum circuits and the application of proof strategies. The system utilizes a combination of techniques including logical deduction, model checking, and constraint solving, adapted for the unique characteristics of quantum computation. The paper outlines the key components of this system and highlights its potential to significantly improve the trustworthiness and reliability of quantum computing technologies. The central aim is to establish a robust framework for automated verification, reducing the risk of errors and accelerating the development of quantum software.
Zero-Knowledge Cryptographic Verification (ZK) represents a significant advancement in secure communication, allowing a prover to demonstrate knowledge without revealing the underlying information. This paper explores a novel approach to ZK verification leveraging the principles of entangled state propagation. We propose a protocol that utilizes entanglement to establish a shared, verifiable state, and employs a quantum-enhanced algorithm to guarantee the state's consistency. This eliminates the need for direct data exchange, offering enhanced security and efficiency compared to traditional cryptographic methods. The core mechanism centers around the creation and manipulation of entangled states, which are then used to build a verifiable proof. This paper provides a detailed theoretical analysis and preliminary implementation of this protocol, demonstrating its potential for secure and efficient verification.