Enhancing Quantum Approximate Optimization with CNN-CVaR Integration

Abstract The Quantum Approximate Optimization Algorithm (QAOA) represents a promising approach for tackling combinatorial optimization challenges on near-term quantum devices. Central to QAOA optimization is the minimization of the expectation of the problem Hamiltonian for parameterized trial quantum states, which motivates the exploration of advanced optimization techniques. In this study, we propose a novel combinatorial optimization strategy, CNN-CVaR-QAOA, which integrates a Convolutional Neural Network (CNN) with Conditional Value at Risk (CVaR) to optimize QAOA circuits. By replacing the traditional loss function with CVaR and leveraging CNN for variational quantum parameter optimization, we demonstrate the superior efficacy of CNN-CVaR-QAOA through experimental validation on Erdos-Renyi random graphs. Our results show enhanced approximation ratios across various graph configurations. Furthermore, we investigate the influence of the CVaR parameter (α) on algorithm performance, revealing that lower α values lead to smoother objective functions and improved approximation ratios. CNN-CVaR-QAOA offers significant advantages in optimizing QAOA parameters, particularly in the context of small-scale quantum devices, highlighting its potential to enhance QAOA optimization efforts across diverse optimization domains.