## Abstract

Drawing on the formalism , concepts and techniques of quantum mechanics discussed in Chap. 4, we introduce some of the most important ideas governing quantum computing, starting with an historical overview of this new computational paradigm. Concepts such as the simulation of the laws of physics, coherent superposition, parallelism, entanglement, etc., are briefly described. The basic unit of information in quantum computing, the qubit, is described, along with the restrictions that apply to the qubit and the concept of quantum algorithms. The definition of the single qubit leads to the problem of systems with *n* qubits, for which we recall the concepts of Hilbert spaces and the orthogonal basis, which enable such systems to be appropriately represented. A central issue in quantum computing is then addressed, namely the problematic measurement of states (directly related to Heisenberg’s uncertainty principle), and we explore how Entanglement affects the measurement of states. Finally, we explore the construction of quantum algorithms, which have to take into account the no-cloning theorem, the reversibility of quantum gates that allow operations with qubits, and the unitary property of quantum transformations. The chapter concludes with the construction and analysis of two quantum circuits, one simulating a quantum exchange by means of CN gates, and the other an architecture that relies on several different gates to simulate a quantum CCN.