Explore a comprehensive lecture on quantum algorithms and their applications from near-term to long-term prospects. Delve into quantum field theory simulations, classical vs. quantum approaches, and key concepts like Hamiltonian simulation and ground-state generation. Examine innovative techniques for state preparation and information extraction from quantum states. Investigate empirical hardness models and their methodology, with a focus on the Hamiltonian Cycle Problem. Gain insights into the future vision for quantum computing and its potential impact on algorithmic problem-solving.