Various symmetry-protected topological phases of quantum spins on a breathing Pyrochlore are discussed by the Quantum Monte Carlo method. ZN Quantized Berry phases( N=2,3,4,6) are directly evaluated and used for the phase characterization. They are discussed in relation to the boundary states as a demonstration of the bulk-edge/boundary correspondence. Sequential Berry phases are defined on boundaries of the boundary (edge of edges due to Hashimoto-Kimura-Wu). It can be new. Have a look at our paper, “Topological Properties of Four-qubit Entangled Phases on the Breathing Pyrochlore Lattice” by Katsumi Aoyagi, Yasuhiro Hatsugai, and Tohru Kawarabayashi, which has been published in J. Phys. Soc. Jpn. 94, 044702 (2025) on March 11, 2025. It’s open !