  We investigate the feasibility for the preservation of coherence and
entanglement of one and two spin qubits coupled to an interacting quantum
spin-1/2 chain within the dynamical decoupling (DD) scheme. The performance is
examined by counting number of computing pulses that can be applied
periodically with period of $T$ before qubits become decoherent, while
identical decoupling pulse sequence is applied within each cycle. By
considering pulses with mixed directions and finite width controlled by
magnetic fields, it is shown that pulse-width accumulation degrades the
performance of sequences with larger number of pulses and feasible magnetic
fields in practice restrict the consideration to sequences with number of
decoupling pulses being less than 10 within each cycle. Furthermore, within
each cycle $T$, exact nontrivial pulse sequences are found for the first time
to suppress the qubit-bath coupling to $O(T^{N+1})$ progressively with minimum
number of pulses being $4,7,12$ for $N=1,2,3$. These sequences, when applied to
all qubits, are shown to preserve both the entanglement and coherence. Based on
time-dependent density matrix renormalization, our numerical results show that
for modest magnetic fields (10-40 Tesla) available in laboratories, the overall
performance is optimized when number of pulses in each cycle is 4 or 7 with
pulse directions be alternating between x and z. Our results provide useful
guides for the preservation of coherence and entanglement of spin qubits in
solid state.
