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Explore the fundamental principles of computational complexity theory in this comprehensive 3-hour lecture delivered at the Summer School on Quantum Computing at the University of Zurich. Delve into the mathematical frameworks that classify computational problems based on their inherent difficulty and resource requirements. Examine key complexity classes including P, NP, BQP, and their relationships to quantum computing paradigms. Investigate how quantum algorithms challenge classical complexity assumptions and discover the theoretical foundations that underpin quantum computational advantages. Analyze the implications of complexity theory for quantum algorithm design and understand the boundaries between classical and quantum computational power. Learn about oracle separations, quantum query complexity, and the role of entanglement in computational complexity. Study important complexity-theoretic results that inform our understanding of quantum supremacy and the potential limitations of quantum computers.
