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Introduction to quantum computing - course RUB 12,160. from Open education, training 18 weeks, about 7 hours per week, date of November 28, 2023.
Miscellaneous / / November 29, 2023
The main objective of the course is to introduce students to the rapidly developing field of science and technology at the intersection of physics and computer science - quantum computing. In recent years, quantum computing devices are gradually leaving physical laboratories and becoming applied developments, which are carried out by the R&D departments of the world's leading IT companies. Quantum algorithms are evolving from intriguing theoretical constructs into applied tools designed to solve complex computational problems. At the same time, the atmosphere of excitement around quantum computing leads to some overestimation of achievements and a clear crisis of inflated expectations from technology from IT specialists on the one hand, and often unfounded criticism from physicists on the other hand. another. However, the number of good educational resources devoted to this complex topic, especially in Russian, is very limited. In our course we will try to create a theoretical basis for students in the field of quantum computing in sufficient volume to allow them to independently understand modern work on this subject.
The course will cover the gate model of quantum computing and universal sets of quantum logic gates. We will talk about the main types of quantum algorithms such as phase estimation algorithm, Shor algorithm and other algorithms based on quantum Fourier transform; Grover's algorithm and quantum search algorithms; quantum variational algorithms. We will discuss in detail the problems of combating decoherence and errors in quantum gates, and the issues of constructing quantum error correction codes. Options for the architecture of a quantum computer that is error-resistant will be considered. We will discuss the fundamental possibility of creating an error-resistant quantum computer and the real state of affairs at the current level of technology development.
Currently, Moscow University is one of the leading centers of national education, science and culture. Raising the level of highly qualified personnel, searching for scientific truth, focusing on humanistic ideals of goodness, justice, freedom - this is what we see today as following the best university traditions Moscow State University is the largest classical university in the Russian Federation, a particularly valuable object of cultural heritage of the peoples of Russia. It trains students in 39 faculties in 128 areas and specialties, graduate students and doctoral students in 28 faculties in 18 branches of science and 168 scientific specialties, which cover almost the entire spectrum of modern university education. Currently, more than 40 thousand students, graduate students, doctoral students, as well as specialists in the advanced training system are studying at Moscow State University. In addition, about 10 thousand schoolchildren study at Moscow State University. Scientific work and teaching are carried out in museums, at educational and scientific practice bases, on expeditions, on research vessels, and in advanced training centers.
Lecture 1. Introduction. Historical perspective and current state of the region. The birth of the quantum computing industry. An idea of the features of quantum computing using the example of the simplest Deutsch algorithm.
Lecture 2. Some questions of the theory of computational complexity. The concept of an algorithm, Turing machine, universal Turing machine. Computable and non-computable functions, stopping problem. Solvability problems, an idea of computational complexity classes. Classes P and NP. Probabilistic Turing machine, class BPP. Problems of recalculating the number of solutions, difficulty class #P. The problem of demonstrating quantum supremacy using the BosonSampling problem as an example.
Lecture 3. Fundamentals of the gate model of quantum computing. Gate model of quantum computing. Elementary quantum logic gates, one-qubit and two-qubit gates. Conditional two-qubit gates, representation of conditional multi-qubit gates in terms of two-qubit gates. Description of measurements in quantum theory, description of measurements in quantum circuits.
Lecture 4. A universal set of quantum logic gates. Discretization of single-qubit gates, universal discrete gate sets. The difficulty of approximating an arbitrary unitary transformation.
Lecture 5. Quantum Fourier transform. Phase estimation algorithm, estimation of required resources, simplified Kitaev algorithm. Experimental implementations of the phase estimation algorithm and applications to the calculation of molecular terms.
Lecture 6. Shor's algorithm. Factorization of numbers into prime factors, Shor's algorithm. Experimental implementations of Shor's algorithm. Other algorithms based on the quantum Fourier transform.
Lecture 7. Quantum search algorithms. Grover's algorithm, geometric illustration, resource estimation. Counting the number of solutions to a search problem. Accelerating solving NP-complete problems. Quantum search in an unstructured database. Optimality of Grover's algorithm. Algorithms based on random walks. Experimental implementations of search algorithms.
Lecture 8. Quantum error correction. The simplest codes. Errors in quantum computing, unlike the classical case. Three-qubit code that corrects the X error. Three-qubit code that corrects the Z-error. Nine-bit Shor code.
Lecture 9. Quantum error correction. Calderbank-Shore-Steen codes. General theory of error correction, error sampling, independent error model. Classical linear codes, Hamming codes. Quantum Calderbank-Shor-Steen codes.
Lecture 10. Error-tolerant calculations. Formalism of stabilizers, construction of KSH codes in the formalism of stabilizers. Unitary transformations and measurements in the formalism of stabilizers. The concept of error-tolerant calculations. Construction of a universal set of error-tolerant gates. Error-tolerant measurements. Threshold theorem. Experimental prospects for the implementation of quantum error correction and error-tolerant calculations.
Lecture 11. Quantum computing for NISQ systems. Quantum variational algorithms: QAOA and VQE. Applications to problems of quantum chemistry. Possibilities of implementation on modern quantum processors, development prospects.
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19/12/2019