This bookpresents a new optimization flow for quantum circuits realization. At thereversible level, optimization algorithms are presented to reduce the quantumcost. Then, new mapping approaches to decompose reversible circuits to quantumcircuits using different quantum libraries are described. Finally, optimizationtechniques to reduce the quantum cost or the delay are applied to the resultingquantum circuits. Furthermore, this book studies the complexity of reversiblecircuits and quantum circuits from a theoretical perspective.