This talk will present kinetic energy and entropy preserving (KEEP) schemes, non-dissipative and stable numerical schemes developed for high-fidelity computations of shock-free compressible flows. The research group that I previously belonged to recently succeeded in conducting LES of the flow around whole aircraft configurations, using the KEEP schemes and an LES wall model. In general, flow computations become unstable when non-dissipative numerical schemes are used. The KEEP schemes, however, have performed stable computations of compressible flows without the aid of artificial viscosity, thanks to their superior kinetic-energy and entropy preserving property. The KEEP schemes have been developed for different types of computational grids, such as block-structured Cartesian grids, curvilinear grids, and unstructured grids, so they can be applied to complex geometries. In addition to the KEEP schemes, recent research works about quantum computations will also be briefly presented.