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arXiv:2311.03097

Quantum-Error-Mitigated Detectable Byzantine Agreement with Dynamical Decoupling for Distributed Quantum Computing

Matthew T. Prest, Kuan‐Cheng Chen

Published Nov 6, 2023• 6 citations
arXivHTMLPDF

Abstract

In the burgeoning domain of distributed quantum computing, achieving consensus amidst adversarial settings remains a pivotal challenge. We introduce an enhancement to the Quantum Byzantine Agreement (QBA) protocol, uniquely incorporating advanced error mitigation techniques: Twirled Readout Error Extinction (T-REx) and dynamical decoupling (DD). Central to this refined approach is the utilization of a Noisy Intermediate Scale Quantum (NISQ) source device for heightened performance. Extensive tests on both simulated and real-world quantum devices, notably IBM's quantum computer, provide compelling evidence of the effectiveness of our T-REx and DD adaptations in mitigating prevalent quantum channel errors. Subsequent to the entanglement distribution, our protocol adopts a verification method reminiscent of Quantum Key Distribution (QKD) schemes. The Commander then issues orders encoded in specific quantum states, like Retreat or Attack. In situations where received orders diverge, lieutenants engage in structured games to reconcile discrepancies. Notably, the frequency of these games is contingent upon the Commander's strategies and the overall network size. Our empirical findings underscore the enhanced resilience and effectiveness of the protocol in diverse scenarios. Nonetheless, scalability emerges as a concern with the growth of the network size. To sum up, our research illuminates the considerable potential of fortified quantum consensus systems in the NISQ era, highlighting the imperative for sustained research in bolstering quantum ecosystems.

DOI
10.48550/arxiv.2311.03097

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In distributed quantum computing (DQC), achieving consensus with adversarial elements presents a critical challenge. This paper proposes an innovative framework that enhances the Quantum Byzantine Agreement (QBA) protocol by integrating practical quantum error mitigation techniques, specifically Quantum Readout Error Mitigation (QREM) and Dynamical Decoupling (DD). Utilizing Noisy Intermediate-Scale Quantum (NISQ) devices, our approach aims to improve operational reliability significantly. Our results demonstrate that QREM and DD effectively mitigate common quantum channel errors through rigorous experimentation on both simulated environments and IBM’s quantum hardware. The proposed protocol also introduces a verification mechanism inspired by Quantum Key Distribution (QKD) systems, ensuring the secure transmission of commands encoded in quantum states. In cases of discrepancies, lieutenants engage in systematically designed interactions to achieve consensus, influenced by the Commander’s strategic decisions and the network’s size. Our empirical analysis highlights the protocol’s enhanced resilience and efficiency under various conditions, while also addressing challenges related to scalability as the network size increases.
In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.
This paper presents a novel approach to distributed consensus protocols leveraging quantum entanglement and Byzantine fault tolerance. The core claim is that quantum entanglement can provide secure and efficient agreement among nodes even in the presence of malicious actors. We propose a mechanism that utilizes quantum key distribution (QKD) to establish shared entanglement between participating nodes. Subsequent quantum measurements identify faulty nodes, informing a robust consensus algorithm built upon majority voting and entanglement-based error correction. The potential advantages of this combined approach – enhanced security and efficiency compared to traditional classical methods – are explored. The research addresses the critical challenge of achieving reliable consensus in distributed systems susceptible to Byzantine attacks. This work introduces a new paradigm for consensus, potentially leading to more resilient and secure distributed applications.
Quantum Byzantine agreement (QBA), a cornerstone of quantum blockchain, offers inherent advantages in security and fault tolerance over classical protocols, guaranteed by the laws of quantum mechanics. However, existing multiparty QBA protocols face challenges for large-scale deployment due to exponential communication complexity or reliance on complex multi-particle entanglement. To address this, we propose a multiparty circular QBA protocol that adopts a semi-decentralized architecture, leveraging circular message gathering and quantum digital signatures to achieve quadratic communication complexity and enhanced fault tolerance. Our protocol is experimentally feasible, requiring only weak coherent states, and is compatible with existing star-shaped quantum networks. Simulations conducted on a global satellite-to-ground network demonstrate that the protocol sustains high consensus rates among multiple users, even when employing different key generation protocols under realistic conditions. This work presents a scalable framework for large-scale QBA networks, establishing the foundation for a practical quantum blockchain that enables secure and fault-tolerant decentralized services.
In recent years, there have been significant advancements in various aspects of quantum computing. However, despite this substantial progress, the availability of fault-tolerant quantum computers is still out of reach and may remain so for decades. Therefore, a key challenge is to leverage current NISQ devices to achieve a quantum advantage effectively. In this context, the Quantum Approximate Optimization Algorithm (QAOA) was proposed to potentially demonstrate computational advantages in combinatorial optimization problems using NISQ computers. Meanwhile, quantum error mitigation (QEM) techniques have been developed to address errors, with their effectiveness validated in practical problems involving more than 100 qubits. Therefore, in this paper, we optimize QAOA circuits and apply various error mitigation methods, such as dynamic decoupling and Pauli-twirling, to scale problem sizes on IBM quantum processors. Additionally, we discuss optimal implementation strategies for scalable QAOA. We test our implementations on Max-Cut problems and compare our results with previous works.
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.