Parametrized Quantum Circuit Learning for Quantum Chemical Applications

Abstract: In the field of quantum machine learning (QML), parametrized quantum circuits (PQCs) -- constructed using a combination of fixed and tunable quantum gates -- provide a promising hybrid framework for tackling complex machine learning problems. Despite numerous proposed applications, there remains limited exploration of datasets relevant to quantum chemistry. In this study, we investigate the potential benefits and limitations of PQCs on two chemically meaningful datasets: (1) the BSE49 dataset, containing bond separation energies for 49 different classes of chemical bonds, and (2) a dataset of water conformations, where coupled-cluster singles and doubles (CCSD) wavefunctions are predicted from lower-level electronic structure methods using the data-driven coupled-cluster (DDCC) approach. We construct a comprehensive set of 168 PQCs by combining 14 data encoding strategies with 12 variational ans{\"a}tze, and evaluate their performance on circuits with 5 and 16 qubits. Our initial analysis examines the impact of circuit structure on model performance using state-vector simulations. We then explore how circuit depth and training set size influence model performance. Finally, we assess the performance of the best-performing PQCs on current quantum hardware, using both noisy simulations ("fake" backends) and real quantum devices. Our findings underscore the challenges of applying PQCs to chemically relevant problems that are straightforward for classical machine learning methods but remain non-trivial for quantum approaches.