On the use of hypercube-based quantum walks in one-way quantum key distribution protocols

Quantum Key Distribution (QKD) is a foundational cryptographic protocol that enables two parties to generate and share a secret key with information–theoretic security. However, classical protocols such as BB84, though favored for their simplicity, offer limited resistance to eavesdropping and perform poorly under realistic noise conditions. Recent research has explored the use of discrete–time Quantum Walks (QWs) to enhance QKD schemes. In this thesis, we specifically focus on the one–way QKD protocol introduced by Vlachou et al., where they show that security depends exclusively on the underlying Quantum Walk (QW) parameters, rather than the details of the protocol itself. However, their proposal overlooks alternative graph structures that could offer enhanced noise tolerance and security, considering only one–way QKD protocols on circle–based QWs. In this thesis, we introduce a novel protocol based on QWs over a hypercube topology, and demonstrate that, under identical parameters, it offers significantly improved security and noise resistance compared to the circle–based protocol (i.e., state–of–the–art), thus enhancing protection against eavesdropping. Furthermore, we introduce a flexible, efficient, and extensible simulation framework for one–way QKD protocols based on QWs, supporting both circular and hypercube topologies. Developed using IBM’s software development kit for quantum computing (i.e., Qiskit), our framework supports noise–aware analysis based on realistic noise models. We begin by evaluating the security of the proposed protocol in comparison to the state–of–the–art, demonstrating improved resilience against potential attacks. Additionally, we analyze the maximum Quantum Error Rate (QER) that our protocol can tolerate in the presence of depolarizing and combined amplitude–phase damping noise, using the built–in models provided by the Qiskit framework. In its optimal configuration, the hypercube–based protocol achieves significantly higher noise tolerance than the state–of–the–art, outperforming it by approximately 20% under depolarizing noise and 13% in presence of amplitude–phase damping, assuming identical conditions. To support reproducibility and future developments, we release our entire simulation framework as open–source. This thesis establishes a foundation for both the design and simulation of topology–aware QKD protocols that combine enhanced noise tolerance with topologically driven security.