Quantum computers are emerging as a viable alternative to tackle certain computational problems that are challenging for classical computers. With the rapid development of quantum hardware such as those based on trapped ions, there is practical motivation for identifying risk management problems that are efficiently solvable with these systems. Here we focus on network partitioning as a means for analyzing risk in critical infrastructures and present a quantum approach for its implementation. It is based on the potential speedup quantum computers can provide in the identification of eigenvalues and eigenvectors of sparse graph Laplacians, a procedure which is constrained by time and memory on classical computers.
Quantum computers are emerging as a viable alternative to tackle certain computational problems that are challenging for classical computers. With the rapid development of quantum hardware such as those based on trapped ions, there is practical motivation for identifying risk management problems that are efficiently solvable with these systems. Here we focus on network partitioning as a means for analyzing risk in critical infrastructures and present a quantum approach for its implementation. It is based on the potential speedup quantum computers can provide in the identification of eigenvalues and eigenvectors of sparse graph Laplacians, a procedure which is constrained by time and memory on classical computers.
Graph partitioning is a crucial problem in computer science with applications in diverse areas like VLSI design, image segmentation, and network analysis. Traditional classical algorithms often face significant challenges when dealing with large and complex graphs, leading to increased computational time and memory requirements. This paper explores the potential of quantum walk algorithms to address this issue. We propose a framework for leveraging quantum walk algorithms to efficiently explore the connectivity structure of a graph and identify optimal partitions. The core idea involves mapping the graph's nodes and edges onto a quantum system and utilizing the inherent parallelism of quantum walks to traverse the graph. We present a theoretical analysis of the algorithm's potential speedup compared to classical approaches, focusing on scenarios where quantum computation offers a significant advantage. Specifically, we formulate the graph partitioning problem as a search problem on a graph represented as a quantum walk, considering the Hamiltonian operator and its eigenstates for efficient traversal. The effectiveness of the algorithm is dependent on the graph's structure and the ability to accurately simulate the quantum walk. The presented methodology provides a novel approach to graph partitioning, potentially leading to substantial performance improvements for large, complex graphs.
The complexity of large-scale 6G-and-beyond networks demands innovative approaches for multi-objective optimization over vast search spaces, a task often intractable. Quantum computing (QC) emerges as a promising technology for efficient large-scale optimization. We present our vision of leveraging QC to tackle key classes of problems in future mobile networks. By analyzing and identifying common features, particularly their graph-centric representation, we propose a unified strategy involving QC algorithms. Specifically, we outline a methodology for optimization using quantum annealing as well as quantum reinforcement learning. Additionally, we discuss the main challenges that QC algorithms and hardware must overcome to effectively optimize future networks.
Network verification, broadly defined as proving the correctness of certain properties resulting from a network's configuration, cannot be efficiently solved on classical hardware via brute force. Prior work has developed a variety of methods that scale by observing a structure in the search space and then evaluating classes induced by that structure. However, even these classification mechanisms have their limitations. In this paper, we consider a radically different approach: applying quantum computing to more efficiently solve network verification problems. We provide an overview of how to map variants of verification problems into unstructured search problems that can be solved via quantum computing with quadratic speedup, making the approach feasible in theory to problems that twice as big in the size of the input. Emerging quantum systems cannot yet tackle problems of practical interest, but rapid advances in hardware and algorithm development make now a great time to start thinking about their application. With this in mind, we explore the limits of scale of the problem for which quantum computing can solve network verification problems as unstructured search.
Graph partitioning is a fundamental problem in computer science with applications in diverse fields, including image processing, network analysis, and VLSI design. Traditional graph partitioning algorithms often face significant computational challenges when dealing with large graphs, leading to exponential scaling of execution time. This paper investigates the application of quantum walk algorithms to address this challenge. We propose a framework leveraging quantum walks to explore different graph partitioning configurations, guided by a cost function that quantifies the quality of each partition. The core idea is to use the inherent parallelism of quantum walks to efficiently sample the partition space. The algorithm's performance is evaluated theoretically, aiming to demonstrate a potential speedup compared to classical approaches. This work lays a foundation for further research into quantum graph partitioning algorithms and explores the possibilities of harnessing quantum computing for optimization problems.
Assessing cyber risk in complex IT infrastructures poses significant challenges due to the dynamic, interconnected nature of digital systems. Traditional methods often fall short, relying on static and largely qualitative models that do not scale with system complexity and fail to capture systemic interdependencies. In this work, we introduce a novel quantitative approach to cyber risk assessment based on Quadratic Unconstrained Binary Optimization (QUBO), a formulation compatible with both classical computing and quantum annealing. We demonstrate the capabilities of our approach using a realistic 255-nodes layered infrastructure, showing how risk spreads in non-trivial patterns that are difficult to identify through visual inspection alone. To assess scalability, we further conduct extensive experiments on networks up to 1000 nodes comparing classical, quantum, and hybrid classical-quantum workflows. Our results reveal that although quantum annealing produces solutions comparable to classical heuristics, its potential advantages are significantly hindered by the embedding overhead required to map the densely connected cyber-risk QUBO onto the limited connectivity of current quantum hardware. By contrast, hybrid quantum-classical solvers avoid this bottleneck and therefore emerge as a promising option, combining competitive scaling with an improved ability to explore the solution space and identify more stable risk configurations. Overall, this work delivers two main advances. First, we present a rigorous, tunable, and generalizable mathematical model for cyber risk that can be adapted to diverse infrastructures and domains through flexible parameterization. Second, we provide the first comparative study of classical, quantum, and hybrid approaches for cyber risk scoring at scale, highlighting the emerging potential of hybrid quantum-classical methods for large-scale infrastructures.
Over the last five years, quantum computing has attracted the attention of a wide variety of research fields with the promise of tackling challenges that currently are infeasible for traditional computing techniques. While quantum computing encompasses many different disciplines, such as quantum machine learning and quantum chemistry, recent advances in the subfield of quantum combinatorial optimization are especially interesting for the risk management and reliability optimization community. However, most of the literature on the topic presents abstract case studies based on problems of low complexity, making it difficult to truly assess the technology's current level of maturity. Thus, this paper presents a condensed review and benchmark of quantum combinatorial optimization, focusing the discussion on the Quantum Approximate Optimization Algorithm (QAOA), arguably one of the most promising quantum optimization approaches in the current literature. A case study regarding the identification of important nodes within the context of critical infrastructure is presented to assess the current state and limitations that the QAOA presents for the field. The case study is showcased in a simulated environment, reflecting ideal conditions assuming a perfect (noise-free) quantum computer. The results obtained indicate that a series of practical limitations and challenges arise when using quantum-based combinatorial optimization approaches in a non-abstract case study. A discussion of these limitations and some feasible solutions to explore in the future are presented at the end of the paper.