Explore a comprehensive quantum colloquium lecture on the development of a polynomial-time classical algorithm for noisy random circuit sampling. Delve into the intricacies of quantum random circuit sampling (RCS) and its role in recent "quantum supremacy" experiments. Examine the computational complexity of RCS and learn about a groundbreaking polynomial-time classical algorithm for sampling from noisy random quantum circuits. Understand the implications of this algorithm on the scalability of experimental violations of the extended Church-Turing thesis. Gain insights into the theoretical aspects of the algorithm, including its running time and scaling properties. Investigate recent progress in the field, practical challenges, and power arguments. Participate in a panel discussion featuring experts in quantum computing, exploring the broader implications and future directions of this research.