Abstract
In this paper, we investigate the circuit complexity of a quantum charged particle in an external magnetic field. Utilizing the Nielsen approach, we determine the complexity of thermofield double states as functions of time, temperature, and cyclotron frequency. We analyze both the complexity and the amplitude of its oscillations across various parameter values, and reveal that these results cannot be derived as a limit of the harmonic oscillator case. Finally, we calculate the rate of complexity and show that it obeys the Lloyd bound.