Symmetry-Related Topological Phases and Applications: From Classical to Quantum Regimes

Topological phase has received considerable attention in recent decades. One of the crucial factors to determine the phase is symmetry. Such a concept involves mathematical, geometrical, and physical meanings, which displays many fascinating phases in Hermitian and non-Hermitian systems. In this paper, we first briefly review the symmetry-related topological phases in Hermitian and non-Hermitian systems. The study in this section focuses on the topological phase itself, not the realizations therein. Then, we present a thorough review of the observations about these symmetry-related topological phenomena in classical platforms. Accompanied by the rise of quantum technology, the combination of symmetry-related topological phase and quantum technology leads to an additional new avenue, in which quantum information tasks can be accomplished better. Finally, we provide comments about future research into symmetry-related topological phases.