  Dynamical decoupling has been actively investigated since Viola first
suggested using a pulse sequence to protect a qubit from decoherence. Since
then, many schemes of dynamical decoupling have been proposed to achieve
high-order suppression, both analytically and numerically. However, hitherto,
there has not been a systematic framework to understand all existing uniform
$\pi$-pulse dynamical decoupling schemes. In this report, we use the projection
pulse sequences as basic building blocks and concatenation as a way to combine
them. We derived a new concatenated-projection dynamical decoupling (CPDD), a
framework in which we can systematically construct pulse sequences to achieve
arbitrary high suppression order. All previously known uniform dynamical
decoupling sequences using $\pi$ pulse can be fit into this framework.
Understanding uniform dynamical decoupling as successive projections on the
Hamiltonian will also give insights on how to invent new ways to construct
better pulse sequences.

Quantum Physics