  There has been a very large body of research on searching a marked vertex on
a graph based on quantum walks, and Grover's algorithm can be regarded as a
quantum walk-based search algorithm on a special graph. However, the existing
quantum walk-based search algorithms suffer severely from the souffl\'{e}
problem which mainly means that the success probability of finding a marked
vertex could shrink dramatically even to zero when the number of search steps
is greater than the right one, thus heavily reducing the robustness and
practicability of the algorithm. Surprisingly, while the souffl\'{e} problem of
Grover's algorithm has attracted enough attention, how to address this problem
for general quantum walk-based search algorithms is missing in the literature.
Here we initiate the study of overcoming the souffl\'{e} problem for quantum
walk-based search algorithms by presenting a new quantum walk-based search
framework that achieves robustness without sacrificing the quantum speedup. In
this framework, for any adjustable parameter $\epsilon$, the quantum algorithm
can find a marked vertex on an $N$-vertex {\it complete bipartite graph} with
probability at least $ 1-\epsilon$, whenever the number of search steps $h$
satisfies $h \geq \ln(\frac{2}{\sqrt{\epsilon}})\sqrt{N} + 1$. Note that the
algorithm need not know the exact number of marked vertices. Consequently, we
obtain quantum search algorithms with stronger robustness and practicability.
