Quantum Algorithm for Two-level Systems*

Quantum computers are promisingly the world's future technology. In physics, we take interest in calculating the transition matrix elements. For instance, the rate of emission/absorption for a photon/neutrino in a physical process. In this work, we present a general algorithm to compute the transition rates in two-level systems using IBM Quantum. The transition probability is amplified by using an auxiliary qubit that can drive the system to resonance. Furthermore, the algorithm can prepare the excited state with 100% probability given the ground state of a system.