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Quantum Information Processing

Multi-party quantum Byzantine consensus based on full quantum one-way function

Tao Shang, Yao Tang, Yuanjing Zhang, Kun Zhang, Yazhuo Jiang

Published Dec 24, 2024• 1 citation
Publisher
DOI
10.1007/s11128-024-04621-5

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Byzantine agreement, the underlying core of blockchain, aims to make every node in a decentralized network reach consensus. Classical Byzantine agreements unavoidably face two major problems. One is 1/3 fault-tolerance bound, which means that the system to tolerate f malicious players requires at least 3 f + 1 players. The other is the security loopholes from its classical cryptography methods. Here, we propose a Byzantine agreement framework with unconditional security to break this bound with nearly 1/2 fault tolerance due to multiparty correlation provided by quantum digital signatures. It is intriguing that quantum entanglement is not necessary to break the 1/3 fault-tolerance bound, and we show that weaker correlation, such as asymmetric relationship of quantum digital signature, can also work. Our work strictly obeys two Byzantine conditions and can be extended to any number of players without requirements for multiparticle entanglement. We experimentally demonstrate three-party and five-party consensus for a digital ledger. Our work indicates the quantum advantage in terms of consensus problems and suggests an important avenue for quantum blockchain and quantum consensus networks.
We design and experimentally validate quantum circuits that prepare a quantum resource state which, when combined with authenticated classical communication, enables a protocol for detectable Byzantine broadcast and detectable Byzantine consensus. For the broadcast version of the problem, we propose an efficient leader-follower quantum circuit that prepares this resource state with depth O(logn), using O(n) two-qubit gates and O(n) ancillary qubits. We also develop a majority-based leader-selection scheme, for the consensus version of the problem; the scheme is based on the same leaderfollower quantum circuit and on coherent Hamming-weight computation, which prepares a fictitious leader qubit directly from any initial network state specified by the participant parties. The resulting fictitious leader state is then used as input to the leader-follower circuit to prepare a resource state consistent with majority voting on a common basis, thereby enabling detectable Byzantine consensus. In particular, we prove that, when supplemented with authenticated classical channels for the communication of quantum measurement outputs, the resulting protocols achieve detectable Byzantine broadcast and detectable Byzantine consensus, respectively. Under correct operation, all correct parties output the same value, namely the leader's value or the majority value. In the presence of Byzantine parties or quantum circuit deviations, all correct parties detect the inconsistency and abort. Furthermore, we demonstrate the feasibility of the approach through a proofof-principle implementation on an IBM quantum processor.