This thesis presents an exploration of quantum-classical hybrid algorithms for quantum simulation problems, with a focus on the integration of quantum eigenvalue transformation (QEVT), quantum Monte Carlo methods, and shadow tomography techniques. The study is motivated by the potential for practical quantum advantage through these hybrid algorithms, despite the unattainability of fault-tolerant quantum computers in the near future. The objective is to prepare physical states of interest using QEVT as a state preparation oracle and leverage advancements in the field of quantum algorithms. Our contributions are divided into three main applications: the imaginary time evolution with QEVT, thermal shadows with kernel-based denoisers, and a quantum-informed quantum Monte Carlo method comprising quantum-informed sampling of walkers and quantum-assisted energy evaluation. The results of benchmarking with random Hamiltonians and testing on molecular and quantum spin models are presented. This thesis seeks to make a modest contribution to the development of possible alternatives to quantum-classical hybrid algorithms beyond VQAs, bridging innovative quantum algorithms and well-established classical numerical methods.