Exact quantum dynamics for two-level systems with time-dependent driving

Abstract It is well known that the time-dependent Schrrödinger equation can only be solved exactly in very rare cases, even for two-level quantum systems. Thus, finding the exact quantum dynamics under a time-dependent Hamiltonian is not only fundamentally important in quantum physics but also facilitates active quantum manipulations for quantum information processing. In this work, we present a method for generating nearly infinite analytically assisted solutions to the Schrödinger equation for a qubit under time-dependent driving. These analytically assisted solutions feature free parameters with only boundary restrictions, making them applicable in a variety of precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our approach, it can be readily implemented in various experimental setups involving qubits. Consequently, our scheme offers new solutions to the Schrödinger equation, providing an alternative analytical framework for precise control over qubits.