Dynamic Evolution of Quantum Correlations with PSO Algorithm in the Three-qubit Heisenberg XYZ Model Considering DM and KSEA Interactions

In this paper, we consider the three-qubit Heisenberg XYZ model considering DM interaction and KSEA interaction. We use the concurrence, geometric quantum discord, and local quantum uncertainty between the first and third spin as quantum correlation measures. In the absence of a magnetic field and in the presence of a constant magnetic field, quantum correlations appear sudden death and birth, and exhibit a random behavior. In summary, the Heisenberg XYZ model, no adjustment of the exchange interaction strength, DM interaction strength, KSEA interaction strength, and external magnetic field can eliminate the sudden death and births in the evolution of quantum correlations. Thus, we use the particle swarm optimization algorithm (PSO) to determine the magnetic field strength at each time step to increase the quantum correlation. The numerical simulation results show that the quantum correlation increases and reaches a maximum value by our method, and the quantum correlation remains constant at a maximum even after the external magnetic field is cancelled. This result shows that, for any exchange interaction strength, DM interaction strength, and KSEA interaction strength, the quantum correlations reach a certain value and remain at their maximum after the magnetic field is quenched, once the time-varying magnetic field is properly designed. This result provides sufficient possibilities for the use of Heisenberg spin chains as quantum channel.