2026/2027
Введение в квантовые вычисления и квантовую информацию
ID 1232621
Статус:
Маго-лего
Кто читает:
Департамент прикладной математики
Когда читается:
2 модуль
Охват аудитории:
для всех
Преподаватели:
Ханотел Кристиан Луис
Язык:
английский
Кредиты:
3
Контактные часы:
40
Course Syllabus
Abstract
In recent decades, quantum physics has played a key role in the development of new technologies in areas such as metrology, sensor development, quantum computing, and others. This course introduces the fundamentals of quantum computing and quantum information. It provides an introduction to the fundamental concepts of quantum physics, as well as the necessary mathematical tools for understanding the basic elements of quantum computing. Key concepts such as qubits, quantum gates, and quantum algorithms will be covered. The current state of technologies for implementing quantum computers will also be discussed. This is an introductory course for students with basic knowledge of linear algebra.
Learning Objectives
- to explain the fundamental motivations for quantum technologies, the limits of classical computation, and the key principles of quantum mechanics that enable new paradigms
- to introduce the student the main concepts of quantum mechanics (states, operators, measurements, superpositions, etc.)
- to present the basic mathematical (algebraic) tools used in quantum information and quantum computation using Dirac notation
- to teach the basic structure of a quantum algorithm and its diagramatic representation using the quantum circuit model
- to critically analyze basic quantum algorithms, protocols, or implementation strategies, and make a conclusion on their completeness, correctness, efficiency, and practical feasibility
- to teach how to identify and formulate solutions to problems based on the main definitions, postulates, and theorems of quantum information and computation
Expected Learning Outcomes
- Be able to identify the main areas of development of modern quantum technologies
- Be able to explain the technological and scientific reasons why quantum technologies are considered a pivotal field for the 21st century.
- Be able to describe the operation and significance of the Turing machine as a foundational model of computation.
- Be able to explain the concepts of bits and Boolean logic and how they form the basis of classical computation.
- Be able to illustrate the circuit model of computation by constructing simple logic circuits.
- Be able to explain the basic facts about the physical nature of information
- Be able to explain the main physical principles demonstrated by the Stern-Gerlach and Young's double-slit experiments.
- Be able to state the postulates of quantum mechanics
- Be able to explain the basic concepts: quantum state, superposition, quantum measurement.
- Be able to write simple linear algebra operations in terms of Dirac bra-ket notation. Be acquainted with basic properties of quantum observables, state vectors and density matrix
- Be able to define qubits, quantum gates and to explain the basic construction of the circuit model of quantum computation
- Be able to represent single-qubit and multi-qubit quantum gates using matrix notation and their associated circuit diagrams, the student will be able to recognize the most commonly used quantum gates (Hadamard, Pauli gates, CNOT)
- Be able to explain tu concept of a set of universal quantum gates and why they are necessary for quantum computation.
- Be able to explain the problem solved by Deutsch-Josza, Grover and Shor's algorithm, describing their main steps and be able to analyze the significance of these algorithms in demonstrating the potential for quantum advantage.
- Be able to describe the main physical platforms for implementing quantum computers and explain the defining characteristics of the Noisy Intermediate-Scale Quantum (NISQ) era and its implications for algorithm development.
- Be able to define an entangled state and provide specific mathematical examples (e.g., Bell states)
- Be able to compare and contrast classical information (Shannon entropy) with quantum information (von Neumann entropy) and explain the significance of the Holevo bound.
- Be able to explain the concept of decoherence and its role as a primary obstacle in quantum information processing.
- Be able to describe some of the main applications of quantum information theory (conceptually): data compression, quantum cryptography and quantum communication.
Course Contents
- Motivation: Importance of quantum technologies in the XXI century
- Fundamental concepts of classical computation
- Introduction to quantum mechanics
- Quantum computation
- Quantum algorithms
- Current state of quantum computer implementation
- Quantum information and quantum entanglement
Interim Assessment
- 2026/2027 2nd module0.2 * Quiz + 0.1 * Activity + 0.7 * Final exam (written + oral defense)
Bibliography
Recommended Core Bibliography
- Введение в квантовые информационные технологии, Богданов, Ю. И., 2025
- Квантовые вычисления и квантовая информация, Нильсен, М., 2006
- Квантовые системы, каналы, информация, Холево, А. С., 2010
Recommended Additional Bibliography
- Imai, H., & Hayashi, M. (2006). Quantum Computation and Information : From Theory to Experiment. Berlin: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=170875
- Klaus Petritsch. (2019). Quantum Information Science : The New Frontier in Quantum Computation, Secure Communication, and Sensing. [N.p.]: Arcler Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2013956
- Samuel J. Lomonaco, J., & Howard E. Brandt. (2011). Quantum Computation and Information. [N.p.]: AMS. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=974773