In the conventional combination of logic circuits, energy loss is an important consideration. Research on reversible logic circuits are of interest to power minimization having applications in low power CMOS design, DNA computing, bioinformatics, nanotechnology, information security and so on. In this book, a novel reversible quantum full adder, reversible BCD adder, subtraction and quantum No-Wait-Carry adder and a novel reversible quantum array multiplier is introduced. At the same time, the model of this array multiplier based on CMOS technology and pass-transistor is also discussed. Reversible arithmetic logic unit and a novel 1-bit reversible comparator and another novel 4-bit reversible comparator are described as well. Finally, this book devotes itself to the theory and simulation of QCA, introduces a study of quantum states in semi-classical simulation and the genetic simulated annealing simulation method based on the polarized rule.