The Weak Broadcast protocol is a quantum solution to the Byzantine agreement problem. However, its practical applicability remains uncertain due to the impact of noise in quantum systems. Building on prior work by Guba et al., which presented a quantum Byzantine agreement protocol using a four-qubit singlet state, this research investigates how gate-level noise affects the success probability of the protocol, focusing on a Linear Circuit implementation. Gate noise is a critical challenge in quantum hardware, as quantum gates are a primary source of errors in current devices. Using the NetSquid and SquidASM frameworks, the protocol was reproduced and extended with a realistic depolarizing noise model to simulate noisy conditions across different scenarios. Results show that even modest noise levels (0.001% - 0.01%) lead to a sharp rise in failure probability, and at 1% noise, the protocol fails often. These findings highlight the protocol's vulnerability to gate noise and suggest that its practical deployment would require significant error mitigation and fault-tolerant architectures, or a design adapted to better tolerate gate-level noise. This work offers a reproducible simulation framework and provides insights into the protocol's robustness under noisy conditions, addressing a gap in current literature.

Most classical Byzantine agreement protocols between n nodes offer a fault tolerance t of up to t < n/3. Quantum fault-tolerant consensus protocols have been proposed that achieve a tolerance of t < n/2 and are therefore worth studying. In this paper, we assess the failure probability of a previously proposed quantum-aided weak broad- cast protocol and how it is affected by a physical error source. Specifically, we study the effect of measurement error noise. We simulate the protocol as-is on a four-node quantum network composed of NV-center devices, both with zero and with one faulty node. We then apply a measurement error noise model and compare the failure prob- ability with the noiseless version. The noise "strength" is also varied in order to assess whether the failure probability can be reduced using improved hardware. We show that measurement errors have a significant negative effect on the failure probability of the protocol. In fact, even with 10x improved hardware parameters, the protocol does not achieve an acceptable failure probability.   

The Byzantine agreement problem in computer science focuses on honest parties trying to achieve consensus in a network with malicious actors. The performance of a quantum-aided Byzantine agreement protocol was evaluated under more realistic noise conditions, with a particular focus on gate-level errors. Since quantum systems are affected by various forms of noise, understanding the impact of quantum noise is crucial for assessing the practical viability and robustness of such protocols. Our results indicate a gate error probability threshold of 0.001%, below which the protocol maintains a failure probability of less than 5%. However, only a single source of noise was considered, with the depolarizing probabilities for single- and two-qubit gates assumed to be equal. This noise level closely matches the currently achievable error rate for single-qubit gates, but is over an order of magnitude lower than that for two-qubit gates on quantum network hardware. Consequently, our findings suggest that the protocol, in its current form, requires further research before it can be deployed on existing quantum devices. Moreover, the results strongly indicate that two-qubit gate errors are the primary bottleneck. These results highlight the significant impact of quantum noise on distributed quantum protocols and underscore the need for either improved quantum hardware or enhanced fault-tolerant protocol designs.

The Byzantine agreement problem is a challenge in distributed computing that explores how reliable parties can reach consensus even though there are unreliable or malicious participants. Quantum solutions propose better fault tolerance than the classical solutions, tolerating up to t < n/2 number of faulty or malicious parties, compared to the classical solutions with a limit t < n/3 where n is the number of participating parties. The Weak Broadcast Protocol we study proposes a quantum-aided solution using entangled four-qubit states. However, the hardware imperfections of quantum computers affect the reliability of the protocol. This paper investigates the impact of leakage errors, defined as unintended measurement outcomes that fall outside the set of expected basis states, on the failure probability of the protocol. We simulate the protocol in a noise-free setting using SquidASM to validate our setup and failure probabilities against the results reported in prior work. We then introduce a custom bit-flip leakage noise model, supported by an analytical formulation, and compare it with the pessimistic assumptions on the effect of the leakage errors by the prior work. Our results show that while the protocol’s failure probability increases significantly under leakage noise, it is not as pessimistic as assumed before. The observed behavior differs for different fault configurations and shows that moderate noise may significantly affect the failure probability of the protocol. These findings suggest that the protocol is vulnerable to realistic noise.

Byzantine agreement protocols allow distributed systems to achieve consensus despite faulty nodes. The classical solution to the Byzantine agreement can only tolerate less than 1/3 of the total nodes being faulty, while a quantum-aided protocol has the potential to tolerate up to 1/2 of the nodes being faulty. However, the quantum states used in the protocol are vulnerable to decoherence, a process that results in the degradation of a quantum state. This research investigates how memory decoherence affects the failure rate of a three-party quantum Byzantine agreement protocol. The primary contribution is demonstrating that the protocol is resilient to carbon T2 decoherence, as its Z-basis measurement scheme is insensitive to phase errors. Conversely, the failure probability increases with decreasing carbon T1 decoherence values. Extrapolating from the observed trend of decreasing failure with longer T1 coherence times, the protocol’s performance on nitrogen vacancy center hardware is expected to approach the ideal, noiseless limit due to their experimentally established long T1 times.