Generalized Uhrig Dynamical Decoupling for Multi-Level Quantum Systems

Dynamical decoupling can efficiently suppress decoherence induced by the system-environment interaction. Recently, Uhrig proposed an efficient dynamical decoupling scheme, which uses only $N$ pulses to suppress dephasing noise to $O(T^{N+1})$ for a qubit system with total time evolution $T$. We generalize Uhrig's dynamical decoupling scheme from 2-level to $L$-level quantum systems. We find that $M=(L-1)N$ pulses are sufficient to suppress dephasing noise to $O(T^{N+1})$. We observe interesting patterns in the timing of these pulses, which depend on both $L$ and $N$ with various asymptotic forms for large $L$ or large $N$.