We investigate application of quantum computing algorithms to classifying network traffic and mitigating denial of service and distributed denial of service attacks. Using actual honeynet data, we compare solutions of the Max Cut problem using both the quantum approximate optimization algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Experimental results from a 6-qubit quantum computer show that optimal solutions can be found with about 98% accuracy in polynomial execution time. We found that VQE is more accurate than QAOA (compared with classical brute force solutions) but also requires significantly longer execution times. Simulations predict this approach can scale to much larger quantum computing hardware (when available) and may achieve quantum advantage on hardware with 30-35 qubits.
We investigate application of quantum computing algorithms to classifying network traffic and mitigating denial of service and distributed denial of service attacks. Using actual honeynet data, we compare solutions of the Max Cut problem using both the quantum approximate optimization algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Experimental results from a 6-qubit quantum computer show that optimal solutions can be found with about 98% accuracy in polynomial execution time. We found that VQE is more accurate than QAOA (compared with classical brute force solutions) but also requires significantly longer execution times. Simulations predict this approach can scale to much larger quantum computing hardware (when available) and may achieve quantum advantage on hardware with 30-35 qubits.
This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and greedy heuristics. We develop a theoretical model to analyze the time complexity, scalability, and communication overhead in hybrid systems. Using simulations, we evaluate QAOA's performance on small-scale Max-Cut instances, benchmarking its runtime, solution accuracy, and resource utilization. The study also investigates the scalability of QAOA with increasing problem size, offering insights into its potential advantages over classical methods for large-scale combinatorial optimization problems, with implications for future Quantum computing applications in HPC environments.
ABSTRACT: Even if the quantum computing popularity has recently grown, the currently-available technology is not ready for a fundamental revolution of informatics. In this transition phase, hybrid quantum-classical algorithms can help in understanding the real power that this novel paradigm can reach in the future. In this work, we tested the capability of two such algorithms to solve combinatorial optimization problems: the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA). We used them to solve max-cut problems, consisting of separating the vertices of an undirected graph in two sub-groups so that the number of edges connecting vertices of different sub-groups is maximal. To do that, we mapped the problem into a quantum system, using the Ising formalism. In particular, we investigated the effect of changing the number of measurements of the quantum circuit associated with the system on the algorithms convergence. A large number of measurements (or shots) allows a better knowledge of the quantum state, but on the other hand, increases the convergence time, making the algorithms less competitive compared to classical techniques. The results showed that VQE needs a mínimum number of measurements to start converging towards the optimal problem solution. Once this threshold is overcome, the solution improves as 1/√shots. QAOA, on the other hand, does not seem to converge, independently of the number of shots.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
A novel quantum algorithm named the Quantum Approximate Shift-Phase Algorithm (QASPA) is proposed for the approximate solution of the Max-Cut problem. The Max-Cut problem consists in partitioning the set of vertices into two subsets in such a way that the total weight of the edges connecting vertices from different subsets is maximized. This problem is known to be NP-complete and represents a combinatorial challenge. Classical solution algorithms require excessive computational time, rendering them inefficient for medium and large graphs. Approximate solution methods offer guaranteed approximation ratios but still face significant limitations in terms of accuracy and performance on larger graphs. The proposed algorithm features a simple scheme and a minimal number of optimized parameters. The input graph is represented by an adjacency matrix, after which the edge weights are linearly normalized to fixed phase angles. The quantum circuit begins by applying a Hadamard transform to each qubit, thereby creating an equal superposition of all possible partitions. Subsequently, for each pair of adjacent vertices, a sequence comprising a controlled NOT gate, a single-qubit rotation around the Y-axis by an angle proportional to the edge weight, and a second controlled NOT gate is applied. This encodes the phase information about the edge weights into the quantum state of the system. After circuit execution, the qubits are measured in the standard computational basis, and the resulting probability distribution allows the selection of the most probable partition as an approximate solution to the problem. Experimental studies conducted on quantum processor simulators have demonstrated that the proposed algorithm achieves accuracy comparable to the Variational Quantum Approximate Optimization Algorithm (QAOA) while significantly reducing computation time due to the absence of iterative parameter optimization. Moreover, as the graph size increases, the algorithm's runtime grows considerably slower compared to classical brute-force approaches and QAOA, confirming its potential for solving medium-sized Max-Cut problems.
Modern Cloud/Edge architectures need to orchestrate multiple layers of heterogeneous computing nodes, including pervasive sensors/actuators, distributed Edge/Fog nodes, centralized data centers and quantum devices. The optimal assignment and scheduling of computation on the different nodes is a very difficult problem, with NP-hard complexity. In this paper, we explore the possibility of solving this problem with Variational Quantum Algorithms, which can become a viable alternative to classical algorithms in the near future. In particular, we compare the performances, in terms of success probability, of two algorithms, i.e., Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). The simulation experiments, performed for a set of simple problems, show that the VQE algorithm ensures better performances when it is equipped with appropriate circuitansatzesthat are able to restrict the search space. Moreover, experiments executed on real quantum hardware show that the execution time, when increasing the size of the problem, grows much more slowly than the trend obtained with classical computation, which is known to be exponential.
Quantum supremacy refers to the point at which quantum computers outperform classical high-performance computing (HPC) systems in solving computations that are infeasible for conventional systems. Real-time optimization problems—such as traffic flow, financial modeling, logistics, portfolio balancing, cryptographic simulations, and supply chain design—require massive computation and near-instant decision-making, presenting a strong testbed for demonstrating true quantum advantage. This research evaluates quantum optimization performance using Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), comparing them against classical HPC techniques such as simulated annealing and gradient descent optimization. Benchmarking was conducted using real-time optimization datasets via IBM Quantum processors (127-qubit systems) and NVIDIA A100-based HPC clusters. Results indicate that quantum systems reduced computational complexity and required 54% less time to reach near-optimal solutions in large combinatorial problems involving more than 10¹⁷ possible permutations. Classical systems exhibited latency bottlenecks and exponential time growth, while quantum execution achieved polynomial-time convergence. This study validates quantum supremacy in selective optimization workloads and provides a roadmap for industrial adoption.