Lecture 1. Basic elements in quantum circuits

Quantum circuits are convenient for describing physical processes on quantum systems and for studying the computational power of such systems. Before studying quantum circuits, it is useful to understand what quantum circuits consist of and how they are described mathematically. In this Lecture, we discuss the basic elements used in quantum circuits: classical and quantum bits (qubits), pure and mixed state preparations, unitary gates on qubits, qubit measurements, classical control of gates and channels describing noise. As an example, we describe how the protocol of quantum teleportation works.