Hello everyone. Welcome to the third week, of the course Quantum Computing less formulas', more understanding, brought to you by the faculty of mathematics and mechanics of St. Petersburg State University. We continue to discuss their regions of the mathematical model of quantum computing. On the previous week, we introduced the term wave-function, which refers the quantum mechanical description of a particle. We know now that wave functions for a linear vector space. That in any vector space we can choose an orthonormal basis. The choice of these basis defines what physicists call an observable, which is strongly connected to the properties of our measurement process. Because when we measure some property of the particle using this observable, they always obtain one of the vectors of its basis with the probability defined by amplitude of this vector in the wave function decomposition in these basis. We also discussed the particular observable, which is connected to the measurement of the position of a particle. The basis for this observable is continuous and it consists of so called Dirac's delta functions. This is usually denote this observable with the capital letter R or sometimes Q. The letter comes from Lagrangian mechanics, where small letters q denotes the generalized coordinates of a system. While small b's denote the generalized of momentum. As you can guess, there is the capital letter P, which denotes the observable for the momentum of a particle in quantum mechanics. Let's recall the list of questions we are going to answer. First. What is a Qubit? Why mathematically it is a two dimensional vector? We'll talk about it very soon. Second, what is the superposition state and why is it the source of so called quantum parallelism? Why do we need complex numbers? Then, what is measurement? How the probabilities of the measurement outcomes are calculated, and why so? Actually, this is the only question we have answered on the previous week. Five, how the system of several particles is described? Why do we need denser products for this? At last, what are the entangled states? As you see on last week, we have answered only one of these questions, and all the remaining questions are left for this week. It looks, there's much to learn. Let's do it.