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Chemistry is considered as one of the more promising applications to science of near-term quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Because of the limitations of near-term quantum computers, the most effective strategies split the work over classical and quantum computers. There is a proven set of methods in computational chemistry and materials physics that has used this same idea of splitting a complex physical system into parts that are treated at different levels of theory to obtain solutions for the complete physical system for which a brute force solution with a single method is not feasible. These methods are variously known as embedding, multi-scale, and fragment techniques and methods. We review these methods and then propose the embedding approach as a method for describing complex biochemical systems, with the parts not only treated with different levels of theory, but computed with hybrid classical and quantum algorithms. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with traditional algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future. 

Perovskite oxides (ABO₃) have been widely recognized as a class of promising noble-metal–free electrocatalysts due to their unique compositional flexibility and structural stability. Surprisingly, investigation into their size-dependent electrocatalytic properties, in particular barium titanate (BaTiO₃), has been comparatively few and limited in scope. Herein, we report the scrutiny of size- and dopant-dependent oxygen reduction reaction (ORR) activities of an array of judiciously designed pristine BaTiO₃and doped BaTiO₃(i.e., La- and Co-doped) nanoparticles (NPs). Specifically, a robust nanoreactor strategy, based on amphiphilic star-like diblock copolymers, is employed to synthesize a set of hydrophobic polymer-ligated uniform BaTiO₃NPs of different sizes (≤20 nm) and controlled compositions. Quite intriguingly, the ORR activities are found to progressively decrease with the increasing size of BaTiO₃NPs. Notably, La- and Co-doped BaTiO₃NPs display markedly improved ORR performance over the pristine counterpart. This can be attributed to the reduced limiting barrier imposed by the formation of -OOH species during ORR due to enhanced adsorption energy of intermediates and the possibly increased conductivity as a result of change in the electronic states as revealed by our density functional theory–based first-principles calculations. Going beyond BaTiO₃NPs, a variety of other ABO₃NPs with tunable sizes and compositions may be readily accessible by exploiting our amphiphilic star-like diblock copolymer nanoreactor strategy. They could in turn provide a unique platform for both fundamental and practical studies on a suite of physical properties (dielectric, piezoelectric, electrostrictive, catalytic, etc.) contingent upon their dimensions and compositions.