Noisy Byzantine Agreement Protocol in a Small Quantum Network

Abstract

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.