AccelerQ: Accelerating Quantum Eigensolvers with Machine Learning on Quantum Simulators

We present AccelerQ , a framework for automatically tuning quantum eigensolver (QE) implementations– these are quantum programs implementing a specific QE algorithm–using machine learning and searchbased optimisation. Rather than redesigning quantum algorithms or manually tweaking the code of an already existing implementation, AccelerQ treats QE implementations as black-box programs and learns to optimise their hyperparameters to improve accuracy and efficiency by incorporating search-based techniques and genetic algorithms (GA) alongside ML models to efficiently explore the hyperparameter space of QE implementations and avoid local minima. Our approach leverages two ideas: 1) train on data from smaller, classically simulable systems, and 2) use program-specific ML models, exploiting the fact that local physical interactions in molecular systems persist across scales, supporting generalisation to larger systems. We present an empirical evaluation of AccelerQ on two fundamentally different QE implementations: ADAPT-QSCI and QCELS. For each, we trained a QE predictor model, a lightweight XGBoost Python regressor, using data extracted classically from systems of up to 16 qubits. We deployed the model to optimise hyperparameters for executions on larger systems of 20-, 24-, and 28-qubit Hamiltonians, where direct classical simulation becomes impractical. We observed a reduction in error from 5.48% to 5.3% with only the ML model and further to 5.05% with GA for ADAPT-QSCI, and from 7.5% to 6.5%, with no additional gain with GA for QCELS. Given inconclusive results for some 20- and 24-qubit systems, we recommend further analysis of training data concerning Hamiltonian characteristics. Nonetheless, our results highlight the potential of ML and optimisation techniques for quantum programs and suggest promising directions for integrating software engineering methods into quantum software stacks.