Dynamic decoupling for multi-level systems

Abstract

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