Hybrid Quantum-Classical Density Functional Theory: A Structured Framework

Density Functional Theory (DFT) is widely used for atomistic simulations. However, its reach stays limited due to several limitations such as lack of accurate exchange-correlation functional, requirement of costly O(N 3) diagonalization etc. Although quantum computing offers paths forward, including variational techniques, embedding strategies, and quantum linear solvers, the discussion remains scattered. Without shared terms or structure, evaluating progress in hybrid quantum-classical DFT efforts becomes challenging. To bring order, we introduce a three-axis scheme based on where the method connects into DFT, whether the quantum part boosts precision or cuts time, alongside intended device type: current noisy machines or future error-corrected ones. Sorting known approaches in this way shows why embedding frameworks fit modern tools better, while faster linear algebra waits for more advanced systems.