Quantum thermal state preparation with the repeated interaction protocol

Preparing quantum thermal states on digital quantum computers remains a major challenge, as existing algorithms typically require computational resources that grow exponentially with the size of the system. This limits quantum simulations in many-body physics, chemistry, and materials science. More efficient, scalable methods are thus urgently needed. We approach this problem using the repeated interaction framework, investigating thermalization in simple open quantum systems. We considered a two-level system coupled to an environmental two-level ancilla through an Heisenberg interaction Hamiltonian. We analytically proved that the system reaches a diagonal steady state characterized by an effective temperature different from the bath temperature, and we found analytically exact expressions for the system steady-state population and for the rate of approaching it. Thermalization at bath temperature is recovered if long and weak interactions are considered. We extended our analysis to the scenario where the system is coupled to two baths via non-commuting operators, such that one bath is purely dephasing. We found that the dephasing bath may either accelerate or suppress both population and coherence dynamics. Our results offer valuable insights into potential design principles for more efficient quantum thermalization algorithms with controllable thermalization speed.