Strongly-correlated quantum magnets exhibit a wide variety of exotic quantum phases and non-conventional quantum phase transitions. In theoretical studies of such many-body phenomena, powerful numerical simulation techniques, such as the quantum Monte Carlo method, exact diagonalization, tensor network method, have played an essential role. Our group has developed novel Monte Carlo and related simulation techniques, e.g., O(N) Monte Carlo method for long-range interacting systems, rejection-free Monte Carlo method using irreversible kernel, loop cluster quantum Monte Carlo method for general spin systems, quantum Monte Carlo level spectroscopy based on precise gap measurement, so far. This project is aiming at investigating various quantum phases in strongly-correlated spin systems. Possible targets are the symmetry protected topological phase in one- and two-dimensional quantum spin system, topological phase in quantum dimer model, entanglement spectra at quantum critical point, by using state-of-the-art quantum Monte Carlo technique or other simulation algorithms. The project may also include development of new algorithms and open-source simulation software.