## Fidelity evolution of the single-qutrit dissipative model under control with a different environment memory parameter γ

**Figure 5.** Fidelity evolution of the single-qutrit dissipative model under control with a different environment memory parameter γ. We apply two-layer nesting UDD control sequences with the outer layer *N*_{1} = 20 and the inner layer *N*_{2} = 10. The initial state |\psi (0)\rangle =\frac{1}{\sqrt{3}}(|0\rangle +|1\rangle +|2\rangle ).

**Abstract**

In this paper, we use the quantum state diffusion (QSD) equation to implement the Uhrig dynamical decoupling to a three-level quantum system coupled to a non-Markovian reservoir comprising of infinite numbers of degrees of freedom. For this purpose, we first reformulate the non-Markovian QSD to incorporate the effect of the external control fields. With this stochastic QSD approach, we demonstrate that an unknown state of the three-level quantum system can be universally protected against both coloured phase and amplitude noises when the control-pulse sequences and control operators are properly designed. The advantage of using non-Markovian QSD equations is that the control dynamics of open quantum systems can be treated exactly without using Trotter product formula and be efficiently simulated even when the environment is comprised of infinite numbers of degrees of freedom. We also show how the control efficacy depends on the environment memory time and the designed time points of applied control pulses.