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IEEE International Conference on Nanotechnology (IEEE-NANO)

Quantum circuit and Byzantine generals problem

Chia-Hung Chien, Tein-Sheng Lin, Chin-Yung Lu, Shih‐Yi Yuan, Sy‐Yen Kuo

Published Aug 1, 2012• 2 citations
Publisher

Abstract

This paper designs quantum circuit to detect the fault components in the Byzantine generals problem. This circuit is verification circuit that can investigate the equivalence of quantum input particles. In this problem, reach agreement and liar detection are two major issues. In the quantum field, quantum secret sharing can support a special correlation among sharing party. By using this relation, quantum circuit can detect the behavior of the traitor to obtain the consistence of the Byzantine agreement. In regard to the performance, quantum solution can obtain little message exchange and more tolerant faulty components. Furthermore, the proposed circuit is scalable.

DOI
10.1109/nano.2012.6322082

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This paper designs quantum circuit to detect the fault components in the Byzantine generals problem. This circuit is verification circuit that can investigate the equivalence of quantum input particles. In this problem, reach agreement and liar detection are two major issues. In the quantum field, quantum secret sharing can support a special correlation among sharing party. By using this relation, quantum circuit can detect the behavior of the traitor to obtain the consistence of the Byzantine agreement. In regard to the performance, quantum solution can obtain little message exchange and more tolerant faulty components. Furthermore, the proposed circuit is scalable.
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.
This paper proposes a novel approach to distributed consensus that leverages quantum key distribution (QKD) for Byzantine fault tolerance. Traditional consensus algorithms struggle to guarantee agreement in the face of malicious actors introducing Byzantine faults. This work introduces a framework where a shared secret, established via QKD, serves as the foundation for a consensus protocol. The inherent cryptographic properties of QKD – specifically its ability to detect eavesdropping – are exploited to identify and neutralize malicious nodes attempting to disrupt the consensus process. We demonstrate that this combination offers a fundamentally more secure and efficient solution compared to classical approaches. The core of our system relies on the creation of a quantum-secured shared key, denoted as *K*, and the subsequent implementation of a consensus protocol designed to operate on this key. This protocol incorporates mechanisms for key verification and anomaly detection, providing robust resilience against Byzantine faults. The theoretical analysis presented highlights the advantages of this approach in terms of security and efficiency. We define the following key variables: *n* - number of nodes in the network; *f* - maximum number of faulty nodes; *m* - number of correct nodes; *si* - the state of node *i* (1 if active, 0 if faulty); *K* - the quantum key shared among the nodes; *ri,j* - the raw key shared between nodes *i* and *j*; *Ei,j* - the error rate observed between nodes *i* and *j* during QKD; *σi,j* - the quantum state used for key exchange between nodes *i* and *j*; *Ci,j* - the ciphertext generated during the QKD process; *Di,j* - the decrypted ciphertext between nodes *i* and *j*; *Hi,j* - the hash value calculated based on the decrypted ciphertext. The system's robustness is directly proportional to the level of security provided by QKD and the effectiveness of the consensus protocol in detecting and isolating faulty nodes.
This paper proposes a novel distributed consensus algorithm utilizing quantum entanglement to achieve Byzantine fault tolerance. Traditional consensus algorithms struggle to guarantee correctness in the face of malicious actors (Byzantine faults) where nodes can arbitrarily deviate from the honest majority. This work introduces a protocol that leverages the unique properties of quantum entanglement to establish correlated states between nodes, enabling the detection and mitigation of these malicious behaviors without relying on trusted third parties or computationally intensive verification processes. The core claim is that quantum entanglement provides a provably secure and efficient mechanism for distributed consensus, offering superior resilience compared to classical approaches. The algorithm is formally described, and key mathematical components, including state transformations and probability calculations, are presented. The theoretical analysis demonstrates the algorithm's ability to converge to a correct consensus state even when a significant fraction of nodes are faulty. The use of entanglement fundamentally alters the Byzantine fault tolerance landscape, offering a pathway towards more robust and secure distributed systems.
In distributed computing,Byzantine agreement is a practical method to solve its fault-tolerance problem.There is a variation of the Byzantine agreement which is called detectable Byzantine agreement.This kind of protocol is unsolvable by classical means,but can be solved using quantum resources——quantum entangled states.A typical quantum detectable Byzantine agreement is the GBKCW protocol.The part with the generation and distribution of the lists in the GBKCW protocol was dealed with.In order to keep the GBKCW protocol from the intercept-and-resend strategy,the property of the determination of entangled states were employed to test the sharing state between the parties.
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.