Quantum-derived molecular fingerprints using Hamiltonian simulation for data-driven coupled-cluster approach
\(^{1}\) Department of Chemistry, University of Calgary, Calgary, Canada and Institute for Quantum Science and Technology (IQST), University of Calgary, Canada
\(^{2}\) Faculty of Graduate Studies, University of Calgary, Canada
\(^{3}\) The Edward S. Rogers Sr. Department of Electrical & Computer Engineering, University of Toronto, Canada and Department of Chemical and Physical Sciences, University of Toronto, Mississauga, Canada
\(^{4}\) Centre for Molecular Simulation, University of Calgary, Canada
In quantum chemistry, Coupled-Cluster theory is used to solve the electronic Schrödinger’s equation and obtain accurate energies of molecular systems. Solving the coupled-cluster equations requires iteratively finding the optimal one-electron (\(t_1\)) and two-electron (\(t_2\)) excitation amplitudes. However, obtaining these parameters scales greater than O(\(N^6\)), creating a significant computational bottleneck that limits the method’s applicability to large molecular systems. To address this, the Data-Driven Coupled-Cluster (DDCC) approach was developed to accelerate the computation of \(t_1\) and \(t_2\) amplitudes by utilizing a machine learning framework that only requires input features derived from relatively cheaper quantum chemistry methods to directly predict the optimal excitation amplitude values. These predicted excitation amplitudes can then be used to efficiently obtain accurate correlation energies at the Coupled-Cluster Singles and Doubles (CCSD) level of theory by either serving as an optimized initial guess for the iterative process (“exact CCSD”) or be introduced directly into the energy expression for CCSD (“approximate CCSD). In this context, Quantum Machine Learning (QML) models offer a powerful alternative to classical models in the DDCC approach for predicting these amplitudes and aligning with the quantum-centric supercomputing paradigm. Since the performance of any ML model is heavily dependent on its input features, we are developing Hamiltonian simulation based algorithms as a means to generate high-fidelity quantum-derived input features, or quantum fingerprints. Our work explores the idea of feeding these quantum-derived features into QML models to predict the \(t_1\) and \(t_2\) amplitudes and benchmark the performance for both exact and approximate CCSD correlation energies. Our approach has the potential to enable the estimation of CCSD-quality energies with significantly reduced iterative overhead and providing a methodology for high-level molecular property predictions on emerging quantum architectures.