I. INTRODUCTION
II. DYNAMICAL DECOUPLING BACKGROUND
A. DD with perfect pulses
B. DD with imperfect pulses
C. Optimizing the pulse interval
D. Superconducting hardware physics relevant to DD
E. What this theory means in practice
III. METHODS
A. Pauli demonstration for long times
B. Haar interval demonstrations
IV. RESULTS
A. The Pauli demonstration result: DD works and advanced DD works even better
B. Haar Interval demonstration Results: DD works on arbitrary states, and increasing the pulse interval can help substantially
C. Saturation of CDD and UDD, and an optimum for UR
V. SUMMARY AND CONCLUSIONS