Quantum Honest Byzantine Agreement as a Distributed Quantum Algorithm

TL;DR

The paper reframes Quantum Honest Byzantine Agreement as a coincidence-driven consensus problem and introduces Associative Measuring Neurons to realize a hybrid quantum/classical neural network for QHBA. It couples a Quantum Binding Commitment-based training scheme to define data and leverages Grover-inspired amplitude amplification within the neuron circuitry. A detailed Calculations section analyzes IBM Q Melbourne hardware feasibility, estimating a current practical limit of about $|P| \approx 6$ participants and a potential scale to roughly $85$ with future coherence improvements, highlighting the gap between today and scalable quantum consensus. The work discusses cryptographic benefits from quantum randomness and quadratic speedups, arguing for a pragmatic hybrid architecture that can operate across evolving quantum hardware and secure channels.

Abstract

We suggest that the Quantum Honest Byzantine Agreement (QHBA) protocol [1] essentially reduces consensus to coincidence. The volume of coincidence is the parameter that drives a receiver to echo its input. A lack of coincidence results in no output from a receiver. This is a similar mechanism therefore to the learning mechanism in cognitive modular neural architectures like Haikonen's architecture [2]. We introduce a simple feedback mechanism and quantum neuron to realize a hybrid quantum / classical machine learning network of simple nodes.