Explore approximate quantum compilation with tensor networks in this 16-minute tutorial that introduces the AQTensor tool for building more efficient quantum circuits. Learn how to compress portions of deep circuits, such as Trotterized time evolution, into shorter approximations that preserve essential physics while enabling quantum dynamics studies at larger scales than classical methods or current hardware permit. Discover the key concepts behind this hybrid quantum-classical technique and understand its significance for chemistry, materials science, and high energy physics applications. Follow along as Bryce Fuller demonstrates practical implementation of AQTensor in Qiskit through a hands-on study of the Heisenberg model, providing you with the knowledge to apply approximate quantum compilation techniques to your own quantum simulation problems.