Dynamic decoupling for multi-level systems

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 systems such as qubits and often consists specifically engineered sequences of π pulses that swap between two different states. On the other hand, researchers have gone beyond simple two-levels systems seeking 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 some of them being implemented successfully. However, decoherence in such multi-level systems is inherently more sophisticated than that in two-level systems. So far there has been little systematic research on how to tackle decoherence issues in such systems. In this work, we propose several sequences of dynamical decoupling for 19 multi-level systems that only rely on π pulses linking neighboring levels, which is experimentally friendly. 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 the effect of them on generic Gaussian noise that may not be quasi-static. We also give a physical interpretation 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 represents a first step towards a more systematic investigation of dynamical decoupling techniques applicable to multilevel systems.