Quantum information and quantum computations are a new and rapidly developing branch of physics derived from quantum mechanics, mathematical physics, and classical information theory. The high level of interest in this area is explained by the vast opportunities that will arise from the implementation of its ideas, which will encompass almost all areas of human activity related to the transfer, storage, and processing of information.
The goal of this course is to demonstrate the fundamental concepts of quantum informatics, as well as physical laws and fundamental mathematical principles. Quantum entanglement, quantum parallelism, and quantum interference have received a lot of attention. Most known quantum protocols and algorithms are based on these phenomena, which are covered in separate sections of this course. The course will teach students about quantum teleportation, quantum algorithms, quantum error correction, and other topics related to quantum computations theory.
As a result of the course, students will be able to master the modern mathematical apparatus of quantum mechanics used in quantum computations, as well as the ideas underlying the most important quantum logic algorithms and protocols for transmitting and processing quantum information, and how to solve problems on these topics.
The course is divided into two sections by six modules. The first section (Modules 1-2) is concerned with the mathematical apparatus and the foundations of Quantum Mechanics. The physical laws and processes that underpin quantum computations are thoroughly described. In the second part of the course (Modules 3-6), we demonstrate how to implement quantum computations, quantum logic algorithms, and quantum information transfer protocols using the laws of quantum physics and phenomena discussed in the first part. In the second part of the course (Modules 3-6), we demonstrate how to implement quantum computations, quantum logic algorithms, and quantum information transfer protocols using the laws of quantum physics and phenomena discussed in the first part.
Basic requirements :
Solid knowledge of linear algebra and calculus, as well as an understanding of atom and quantum physics. There is a growing interest in quantum physics and quantum information theory.
Module 1: Quantum mechanics statistical aspects The term "Qubit" refers to a type of A qubit's physical implementation. Qubits are a type of quantum unit of information. Bloch's Sphere Quantum systems can exist in both pure and mixed states. The density matrices and their properties System of qubits Quantum systems are inseparable. The matrix of reduced density.
Module 2 : Entanglement in quantum mechanics. Decomposition according to Schmidt Bell declares. The EPR paradox Bell inequalities are a type of inequity.
Module 3 : Logical operations that are both classical and quantum in nature. Principles of classical computations in general. The most basic classical computations. The Landauer principle Gates that can be reversed. Pauli matriculates. Logic gates with a single qubit. Quantum logic gates that can be controlled.
Module 4.Distinctivefeaturesofquantumcomputations. No-cloningtheorem. Superdense coding. Quantumteleportation. Experimentonqubitquantumteleportation. Quantumparallelism.
Module 5. Quantum Algorithms. Deutsch algorithm. Deutsch–Jozsa algorithm. Quantum Fourier Transform. Eigenvalue algorithm. Shor's algorithm for integer factorization.
Module 6.Basics of error correction theory. Distinctive features of classical error correction theory. Classical three-bit code. Distinctive features of quantum error correction theory. Three-qubit code. Learning outcomes
The student who has completed this course should be familiar with the following concepts :
- fundamental concepts of quantum mechanics and quantum information theory;
- The most important protocols for quantum information transfer and processing;
- The most crucial quantum logic algorithms
- The fundamental protocols of classical and quantum error correction theory
To be able to
- work with classical and quantum circuits;
- solve quantum information theory problems
- quantum mechanics mathematical apparatus used in quantum information theory
1. Statistical aspects of quantum mechanics
- Qubit. Physical implementations of qubit
- Qubit as a quantum unit of information. The Bloch sphere
- Pure and mixed states of quantum systems
- Density matrix and its properties
- Qubit systems. Inseparability of quantum systems
- Reduced density matrix. Part 1
- Reduced density matrix. Part 2
2. Quantum entanglement
- Schmidt decomposition
- Bell states
- EPR paradox
- Bell inequalities
3. Classical and quantum logical operations
- General principles of classical computations
- The simplest classical computations
- Landauer principle. Reversible gates
- The Pauli matrices
- Single-qubit logic gates
- Controlled quantum logic gates
4. Distinctive features of quantum computations
- No-cloning theorem
- Superdense coding
- Quantum teleportation
- Experiments on quantum teleportation of a qubit
- Quantum Parallelism
5. Quantum algorithms
- Deutsch algorithm
- Deutsch–Jozsa algorithm
- Quantum Fourier Transform
- Eigenvalue algorithm
- Shor's algorithm for integer factorization. Part 1
- Shor's algorithm for integer factorization. Part 2
6. Basics of error correction theory
- Features of classical error correction theory
- Classical three-bit code
- Features of quantum error correction theory
- Three-qubit code