With the drive to create a decentralized digital economy, Web 3.0 has become a cornerstone of digital transformation, developed on the basis of computing-force networking, distributed data storage, and blockchain. With the rapid realization of quantum devices, Web 3.0 is being developed in parallel with the deployment of quantum cloud computing and quantum Internet. In this regard, quantum computing first disrupts the original cryptographic systems that protect data security while reshaping modern cryptography with the advantages of quantum computing and communication. Therefore, in this paper, we introduce a quantum blockchain-driven Web 3.0 framework that provides information-theoretic security for decentralized data transferring and payment transactions. First, we present the framework of quantum blockchain-driven Web 3.0 with future-proof security during the transmission of data and transaction information. Next, we discuss the potential applications and challenges of implementing quantum blockchain in Web 3.0. Finally, we describe a use case for quantum non-fungible tokens (NFTs) and propose a quantum deep learning-based optimal auction for NFT trading to maximize the achievable revenue for sufficient liquidity in Web 3.0. In this way, the proposed framework can achieve proven security and sustainability for the next-generation decentralized digital society.