ABSTRACT
This chapter introduces Boolean quantum gates that allow us to map any Boolean circuit in such a way that the circuit becomes reversible. It describes quantum gates for one qubit, like for example Clifford gates that are the elements of the Clifford group and can be efficiently simulated with a classical computer. The chapter introduces the controlled-U gates and the unitary decomposition and formulate the process of transpilation. A Boolean quantum circuit represents a permutation in Hilbert space and can be represented by a unitary permutation matrix composed of the unitary matrices representing the quantum gates. Such a mapping does not alter the distribution of the amplitudes; the distribution remains unchanged during the execution of the quantum Boolean gates.
