Dynamic decoupling for multi-level systems

<sec>Dynamical decoupling refers to a family of techniques that are widely used suppress decoherence in various quantum systems, caused by quasi-static environmental noise. They have broad applications the field information processing. Conventional dynamical targets at noise two-level system such as qubits and often consists specifically engineered sequences <inline-formula><tex-math id="M1">\begin{document}$ \pi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20222398_M1.jpg"/><graphic xlink:href="10-20222398_M1.png"/></alternatives></inline-formula> pulses swap between two different states. On other hand, researchers do not limit their study within simple two-levels systems any more, but go seek for even more efficient hardware. A variety algorithms schemes control using multi-level qutrits qudits, processing been proposed implemented successfully. However, is inherently sophisticated than systems. So far there has little systematic research on how tackle problems systems.</sec><sec>In this work, we propose several only rely id="M2">\begin{document}$ xlink:href="10-20222398_M2.jpg"/><graphic xlink:href="10-20222398_M2.png"/></alternatives></inline-formula> linking neighboring levels, which easy implement experimentally. Our results show these can efficiently presented In addition, calculating corresponding filter functions sequences, able further analyze effect generic Gaussian may be quasi-static. We also give physical explanation filtering mechanism considering functions. Other topics discussed our work include power spectral density correlation regarded first step towards investigation applicable systems.</sec>