Quantum Compilation: Synthesis and Decomposition

This lecture covers the fundamentals of quantum computing, qubit realization, control, and scalable quantum computers. It delves into quantum compilation, error correction, unitary synthesis, permutation synthesis, oracle synthesis, and hierarchical synthesis. The instructor discusses synthesizing single-qubit unitaries, translating between rotations, approximate and exact single-qubit unitary synthesis, uniformly-controlled quantum gates, quantum Shannon decomposition, and the embedding of irreversible functions. Various decomposition-based synthesis methods are explored, including ideal and example-based approaches. The lecture concludes with insights into mapping LUT networks into quantum circuits, FPGA functionality in cryogenic environments, and FPGA-based analog-to-digital converters.