Provide a detailed exploration of the theoretical limits of computation. Discuss the Church-Turing thesis and its implications for what problems are algorithmically solvable. Explain major complexity classes (P, NP, NP-complete, PSPACE, etc.) and their relationships. Analyze the P vs. NP problem, its significance, and major approaches to solving it. Discuss quantum computing and its potential implications for these theoretical limits, including quantum algorithms that offer speedups for certain problems and the classes BQP and QMA.