  Derandomization is the process of taking a randomized algorithm and turning
it into a deterministic algorithm, which has attracted great attention in
classical computing. In quantum computing, it is challenging and intriguing to
derandomize quantum algorithms, due to the inherent randomness of quantum
mechanics. The significance of derandomizing quantum algorithms lies not only
in theoretically proving that the success probability can essentially be 1
without sacrificing quantum speedups, but also in experimentally improving the
success rate when the algorithm is implemented on a real quantum computer.
  In this paper, we focus on derandomizing quanmtum algorithms for the triangle
sum problem (including the famous triangle finding problem as a special case),
which asks to find a triangle in an edge-weighted graph with $n$ vertices, such
that its edges sum up to a given weight.We show that when the graph is promised
to contain at most one target triangle, there exists a deterministic quantum
algorithm that either finds the triangle if it exists or outputs ``no
triangle'' if none exists. It makes $O(n^{9/7})$ queries to the edge weight
matrix oracle, and thus has the same complexity with the state-of-art
bounded-error quantum algorithm. To achieve this derandomization, we make full
use several techniques:nested quantum walks with quantum data structure,
deterministic quantum search with adjustable parameters, and dimensional
reduction of quantum walk search on Johnson graph.
