The application of quantum computation to accelerate machine learning
algorithms is one of the most promising areas of research in quantum
algorithms. In this paper, we explore the power of quantum learning algorithms
in solving an important class of Quantum Phase Recognition (QPR) problems,
which are crucially important in understanding many-particle quantum systems.
We prove that, under widely believed complexity theory assumptions, there
exists a wide range of QPR problems that cannot be efficiently solved by
classical learning algorithms with classical resources. Whereas using a quantum
computer, we prove the efficiency and robustness of quantum kernel methods in
solving QPR problems through Linear order parameter Observables. We numerically
benchmark our algorithm for a variety of problems, including recognizing
symmetry-protected topological phases and symmetry-broken phases. Our results
highlight the capability of quantum machine learning in predicting such quantum
phase transitions in many-particle systems