HYBRID HPC-QUANTUM SIMULATIONS: DFT–Quantum Embedding for Molecular System

Scientific simulations in chemistry and materials science require methods that combine large-scale computational scalability with high predictive accuracy. Classical Density Functional Theory (DFT) executed on High-Performance Computing (HPC) infrastructure enables large electronic-structure simulations, but it struggles with strongly correlated systems, bond dissociation, and accurate band-gap predictions due to inherent approximations in exchange-correlation functionals. Conversely, quantum computing naturally captures complex electron correlation and entanglement, yet current Noisy Intermediate-Scale Quantum (NISQ) hardware remains heavily constrained by limited qubit counts, high noise rates, and restricted circuit depths.

To bridge the gap between classical scalability and quantum accuracy, the authors propose a hybrid DFT-Quantum Embedding (QDFT) framework. This architecture splits large molecular systems into two interacting domains: a chemically relevant active space evaluated via a quantum electronic-structure solver, and the remaining system environment treated via classical DFT. The embedding workflow incorporates several key computational steps:

• Active-space selection and density-based system partitioning
• Embedded Hamiltonian construction via projection-based subspace reduction
• Symmetry preservation using spin-penalty augmentation
• Operator mapping and symmetry tapering
• A two-stage self-consistent density mixing and stabilization protocol

By focusing computational effort where electronic complexity is highest, the approach allows quantum algorithms to target localized challenging regions while retaining classical HPC performance for the broader environment.

Systematic evaluation of the framework focuses on noiseless simulations to assess accuracy improvements, convergence behavior, active-space dependence, and HPC scalability without the confounding effects of hardware noise. Detailed computational profiling identifies primary bottlenecks within CPU-based quantum simulation routines. Furthermore, the work develops a QPU runtime-estimation methodology to quantify the execution requirements and resource scaling needed when transferring this hybrid workflow onto actual quantum hardware as technology matures.