Quantum machine learning of molecular energies with hybrid quantum-neural wavefunction†

Quantum computational chemistry holds great promise for simulating molecular systems more efficiently than classical methods by leveraging quantum bits to represent molecular wavefunctions. However, current implementations face significant limitations in accuracy due to hardware noise and algorithmic constraints. To overcome these challenges, we introduce a hybrid framework that learns molecular wavefunction using a combination of an efficient quantum circuit and a neural network. Numerical benchmarking on molecular systems shows that our hybrid quantum-neural wavefunction approach achieves near-chemical accuracy, comparable to advanced quantum and classical techniques. Based on the isomerization reaction of cyclobutadiene, a challenging multi-reference model, our approach is further validated on a superconducting quantum computer with high accuracy and significant resilience to noise.