Beating the fault-tolerance bound and security loopholes for Byzantine agreement with a quantum solution

Byzantine agreement, the underlying core of blockchain, aims to make every node in a decentralized network reach consensus. However, the classical Byzantine agreement faces two major problems. One is the $1/3$ fault-tolerance bound, which means the system to tolerate $f$ malicious nodes requires at least $3f+1$ nodes. The other problem is the security loopholes of its classical cryptography methods. Here, we propose a quantum Byzantine agreement that exploits the recursion method and quantum digital signatures to break this bound with nearly $1/2$ fault-tolerance and provides unconditional security. The consistency check between each pair of rounds ensures the unforgeability and nonrepudiation throughout the whole process. Our protocol is highly practical for its ability to transmit arbitrarily long messages and mature techniques. For the first time, we experimentally demonstrate three-party and five-party quantum consensus for a digital ledger. Our work suggests an important avenue for quantum blockchain and quantum consensus networks.