Quantum Time-Optimal Bang-Bang Control

The flip of quantum spin used as qubit has a significant effect on quantum computing and quantum information. Therefore, we study the dynamics of quantum spin in two-level spin-1/2 system by using Bang-Bang control protocol in this work. Here, system is driven by constant filed $B_{0}$ along z-axis and controlled field $B(t)$ along $\mathrm{x}$ or y-axis. when $\vert B(t)\vert \geq B_{\mathrm{C}}$ is satisfied, the optimal control time and switching time of spin, from state $\vert 1\rangle$ to $\vert 0\rangle$ , of the system with and without amplitude damping or phase damping are given. Our results demonstrate that the fidelity of state of system with amplitude damping is still up to 0.9985 by Bang-Bang control protocol, even if the coupling strength, $\gamma$ , of system with environment is equal to 0.3 and Bang-Bang control protocol is easier than oscillating filed to operate and analyze.