Genetic Algorithm-Based Ansatz Optimization for Post-Variational Quantum Neural Networks

Post-Variational Quantum Neural Networks (PVQNNs) eliminate the need for quantum parameter optimization by employing fixed, non-parametric circuits and shifting all learning to the classical domain, thereby avoiding barren plateaus entirely. However, the performance of PV-QNNs critically depends on the choice of ansatz architecture. In this work, we propose an automatic ansatz optimization framework based on Genetic Algorithms (GAs) that searches for optimal circuit ensembles under discrete constraints of topology, depth, and gate types. Quantum features are extracted efficiently via classical shadows and processed by a shallow classical classifier, preserving the post-variational property. Experimental results on the Fashion-MNIST (0 vs 4) classification task demonstrate that GA-selected ensembles outperform all baselines, achieving 89.0 % accuracy with 8 qubits, exceeding random and manually designed templates by$\mathbf{3}-\mathbf{5} {\%}$. Moreover, GA ensembles achieve up to$1.9 \times$higher accuracy per circuit and$2 \times$higher accuracy per twoqubit gate, while maintaining shallower circuits (6.0 depth vs. 8.6). These results indicate that evolutionary search effectively identifies compact, information-rich quantum circuits, enabling scalable and resource-efficient post-variational learning.