  Quantum computing (QC) is a new computational paradigm whose foundations
relate to quantum physics. Notable progress has been made, driving the birth of
a series of quantum-based algorithms that take advantage of quantum
computational power. In this paper, we provide a targeted survey of the
development of QC for graph-related tasks. We first elaborate the correlations
between quantum mechanics and graph theory to show that quantum computers are
able to generate useful solutions that can not be produced by classical systems
efficiently for some problems related to graphs. For its practicability and
wide-applicability, we give a brief review of typical graph learning techniques
designed for various tasks. Inspired by these powerful methods, we note that
advanced quantum algorithms have been proposed for characterizing the graph
structures. We give a snapshot of quantum graph learning where expectations
serve as a catalyst for subsequent research. We further discuss the challenges
of using quantum algorithms in graph learning, and future directions towards
more flexible and versatile quantum graph learning solvers.
