A quantum partial adiabatic evolution and its application to quantum search problem

This paper presents a framework for quantum partial adiabatic evolution and applies it to re-examine the well-known quantum search problem. We particularly focus on a detailed analysis of the algorithm’s success probability, which serves as a clear criterion for differentiating valid implementations from invalid ones. Specifically, when the time complexity aligns with the optimal quantum computation, the algorithm achieves a substantially high success probability. Conversely, so-called “improved” versions that exceed the quadratic speedup characteristic of quantum computing exhibit a negligibly low success probability with the increase of target elements. These findings underscore the critical importance of selecting the appropriate evolution interval and the correct method for calculating the success probability in studies of quantum partial adiabatic evolution.