Quantum control and quantum speed limits of single-well systems

Achieving precise control and efficient manipulation of different quantum states is one of the most important goals of quantum technology. We study the quantum control and quantum speed limits of single -well systems by taking a harmonic oscillator whose frequency is a power function of time as an example when the transitionless quantum driving is imposed. For different eigenstates, we reveal the effects of control time and power exponent on Bures angle, fidelity, time -averaged cost, and quantum -speed -limit time. We find that the shortest control time for any eigenstate is proportional to the control parameter (i.e., power exponent). For different eigenstates meeting the same high fidelity requirements, it is shown that an optimal control parameter can always be obtained. Our findings provide theoretical support for the rapid and efficient manipulation of quantum states in single -well systems by using shortcut-to-adiabaticity technique experimentally.