Quantum-Centric Alchemical Free Energy Calculations

In this work, we extended the book-ending framework with a hybrid quantum-classical workflow that incorporates configuration interaction (CI) calculations into alchemical free energy (AFE) predictions. In the book-ending approach, the Multistate Bennett Acceptance Ratio (MBAR) is applied along a coupling parameter λ to interpolate the system from molecular mechanics (MM) (λ = 0) to a quantum mechanics (QM) (λ = 1) description, and the resulting correction is added to the classically computed AFE. Building on the standard book-ending workflow, we developed an interface that introduces the CI contribution through two backends: (I) a classical PySCF-based backend; (II) a quantum-centric sample-based quantum diagonalization (SQD) method and its extended version (ext-SQD). This latter approach combines real quantum processing units (QPUs) with classical postprocessing to obtain CI energies and gradients. To validate the proposed infrastructure, we computed the book-ending corrections for the hydration free energies (HFEs) of three small organic molecules: ammonia, methane, and water. These benchmarks demonstrate that the CI-level electronic structure calculations, particularly those performed on a quantum hardware, can be naturally incorporated into AFE workflows. Specifically, the CI-corrected HFEs are in reasonable agreement with experimental values, supporting the feasibility of QPU-accelerated free energy predictions. As quantum devices continue to improve in scale and fidelity, they might offer a practical and scalable route to CI-quality electronic-structure data for systems that are challenging for classical approaches. Integrating these CI energies directly into QM/MM simulations could improve the accuracy of free energy methods for systems where electronic correlation plays a significant role, with potential relevance to large biomolecular systems, enhancing our ability to model molecular recognition, enzyme catalysis, and drug-receptor interactions.