Enabling Classical Detectable Byzantine Broadcast and Consensus Through Quantum Error Correction Circuits

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.