Explore quantum circuit optimization and synthesis in this Stanford seminar featuring Peter Rakyta from Eötvös Loránd University. Delve into the adaptive circuit compression algorithm implemented in the SQUANDER package, capable of synthesizing circuits up to 9 qubits from unitary representations. Learn about the groundbreaking use of data-flow engine (DFE) based quantum computer simulators on Field Programmable Gate Array (FPGA) chips, enabling significant improvements in circuit compression. Discover how this approach achieves an average 97% compression rate while maintaining high fidelity compared to QISKIT. Gain insights into quantum logical gates, fidelity, cost functions, and the challenges of FPGA implementation. Understand the dataflow programming model, quantum gate operations, and performance comparisons. Examine potential improvements and scaling possibilities for higher qubit numbers in this comprehensive exploration of highly optimized quantum circuits.