Shortcut to adiabaticity and holonomic transformation are the same thing

A stable and fast path linking arbitrary pair of quantum states is commonly desired for the engineering protocols inspired by stimulated Raman adiabatic passage, such as shortcut to adiabaticity and holonomic transformation. It has immediate applications in quantum control and quantum computation and is fundamental about the exact solution of a time-dependent Schr\"odinger equation. We construct a universal control framework based on the system dynamics within an ancillary picture, in which the system Hamiltonian is diagonal so that no transition exists among the ancillary bases during the time evolution. Practically the desired evolution path can be obtained by the von Neumann equation for the parametric ancillary bases. We demonstrate that our control framework can be reduced to the nonadiabatic holonomic quantum transformation, the Lewis-Riesenfeld theory for invariant, and the counterdiabatic driving method under distinct scenarios and conditions. Also it can be used to achieve the cyclic transfer of system population that could be a hard or complex problem for the existing methods. For the state engineering over a finite-dimensional quantum system, our work can provide a full-rank nonadiabatic time-evolution operator.