Hello, everyone. Welcome to the last week of the course. Quantum Computing, less formulas, more understanding. Created for you by St. Petersburg State University, the Faculty of Mathematics and Mechanics. The four long weeks have passed and the four informative modules of new knowledge have been consumed. What have we learned up to now? We understand or we pretend to understand what is a quantum mechanical way to look at the universe. We learned to use the term wavefunction instead of any measurable characteristics of a particle. We know how wave functions map into the state spaces, and what is measurement in terms of quantum mechanics. We learned the term observable, and we understand why in quantum mechanics we use separators while in classical mechanics, we use scholar functions. We learned the term qubit, which is the state of a quantum system with two-dimensional state space. We know how qubits are described and what are the superposition states. Now, at last, we are ready to use this enormous stack of knowledge to do something useful. In this last week, we are going to learn some very basic quantum algorithms which employ everything we learned before. I choose for you not just any basic algorithms, but those that are really useful. So useful that some of them are implemented on the industrial scale. The syllabus for this week is this; first, we are going to consider an algorithm for quantum data transmission or teleportation. You all got used to the simplicity with which we can transfer and copy classical data. But in the case of quantum data, there's an obstacle called the no-cloning theorem. This theorem for [inaudible] of an unknown quantum state. We need something completely different when we want to employ distributed computations in the quantum case. After teleportation, we will be rated to approach the quantum cryptographic algorithms. You probably know that there is a quantum algorithm which can be used for factoring of being composite numbers. It was invented in 1994 by American mathematician, Peter Shor. My course is called the Introduction to Quantum Computing. The whole fourth week is dedicated to the Shor's result. Unfortunately, this algorithm puts in danger widely used asymmetric cryptography algorithm, RSA, which is very popular for the task of gate distribution. This would be unfair to break classical cryptography and not to provide something else in its place. In this model, we will discover two basic but really useful quantum protocols. Any of which can substitute RSA for the task of creation of the shared secret keys. These are BB84 protocol, invented by Charles Bennett and Gilles Brassard in 1984, and E91 protocol invented by Artur Ekert in 1991. Well, enough for the introduction. Let's start learning.