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International Conference on Next-Gen Quantum and Advanced Computing: Algorithms, Security, and Beyond (NQComp)

Quantum-Enhanced Network Flow Optimization: A Max-Flow Min-Cut Perspective

Gagan Guruprasad Phadke, Vandana M. Ladwani

Published Mar 5, 2026• 0 citations
Publisher

Abstract

This paper is a comparison between classical and quantum inspired methods for solving the max-flow problem, which is commonly a foundational challenge in optimization and graph theory. This study will investigate the feasibility and performance of applying the Quantum Approximate Optimization Algorithm (QAOA) and other hybrid quantum-classical approaches to address the max-flow problem. This paper starts with comparing quantum approaches with well-established classical methods such as the Ford-Fulkerson and Edmonds-Karp.The main aim of this work is to asses how close quantum-inspired formulations can get to classical approaches in terms of their flow value as well as their runtime. Implementations are developed using the Qiskit framework on simulated quantum backends and compared against classical baselines across synthetic graph instances of varying sizes and densities. Experimentally, it can be seen that quantum approaches implemented using the QAOA technique managed to attain flow solutions comparable to classical ones, demonstrating similar accuracy, and in certain very dense graph configurations, competitive runtime performance due to parallelization in state-vector computing.These findings suggest that although current quantum-inspired approaches may not yet surpass classical algorithms in efficiency, but they can replicate their outcomes with reasonable fidelity. This provides an important validation of their applicability to combinatorial optimization. This study also lays groundwork for future research to explore hardware-level implementations, scalability enhancements, and also hybrid integration strategies for quantum optimization in network flow problems.

DOI
10.1109/nqcomp68334.2026.11497679

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This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.