Explore the concept of quantum "supremacy" in this comprehensive lecture from Carnegie Mellon University's Quantum Computation course. Delve into topics such as fault tolerance, error-correcting codes, quantum threshold theorem, and quantum error correction. Examine the quantum supremacy plan, random unitary matrices, KL divergence, and uniform distribution. Analyze the challenges and considerations in achieving quantum supremacy, including cross-entropy difference. Gain insights from Professor Ryan O'Donnell's expertise in this advanced exploration of quantum computation and information.