Practical Iterative Quantum Consensus Protocol With Sharding Construction

With the development of quantum blockchain, the quantum consensus protocols have garnered increasing attention, which play a crucial role in driving the implementation of quantum blockchains. However, existing protocols, derived from the classical consensus algorithms, face practical application challenges due to current quantum technology limitations. The first challenge is the bottleneck in generating large-scale entangled quantum states. The second challenge arises from the generation of malicious quantum states. The final challenge involves privacy concerns. To address these challenges, we propose a practical iterative QUantum consensus protocol with sharding construction, namely, Q-Union. In fact, Q-Union employs an iterative consensus algorithm where participating nodes are divided into multiple smaller shards, with the consensus process occurring within the current shard, and new shards are involved only if consensus is not achieved. Leveraging Greenberger-Horne-Zeilinge states and Aharonov states, Q-Union harnesses the advantages of quantum mechanics to achieve anonymous consensus, protecting the private information of participating nodes. Additionally, by integrating state verification, Q-Union ensures the correctness of the consensus procedure in the presence of malicious nodes generating adversarial quantum states. Finally, it is proven that Q-Union can also defend against Byzantine attacks from adversarial nodes, maintaining the same security level as traditional non-sharded consensus protocols. Specifically, it consistently outputs the correct consensus when the fraction of adversaries among participating nodes is less than $1/2$ with synchronous communication. Both the theoretical analysis and performance illustration demonstrate the superior performance of the proposed Q-Union compared to state-of-the-art protocols.