Scalability Challenges in Variational Quantum Optimization under Stochastic Noise

Abstract: With rapid advances in quantum hardware, a key question is whether quantum devices without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. While reports of their challenges and limitations continue to accumulate, many studies still convey optimism based on small-scale toy problems and idealized testing setups. However, doubts remain about the scalability of VQAs and hence their viability for real-world problems. We systematically investigate this scaling behavior by analyzing how state-of-the-art classical optimizers minimize well-behaved quantum loss functions for random QUBO problem instances. Special emphasis is placed on how these algorithms handle uncertainties, modeled as effective Gaussian noise. Our findings reveal that the critical noise threshold, beyond which classical optimizers fail to find optimal or near-optimal solutions, decreases rapidly with system size. This effect exceeds what can be attributed to barren plateaus, indicating more fundamental limitations inherent to the hybrid paradigm of VQAs. When translating this threshold to the finite sampling error permissible in a fault-tolerant scenario, the required number of measurement shots becomes prohibitively high, even for medium-sized problems. These results raise serious doubts about the feasibility of achieving a practical quantum advantage in optimization using VQAs. Instead, they highlight the urgent need to explore fundamentally different algorithms and problem domains that can overcome the reported scalability challenges.