Introduction to Quantum Computing

This online course introduces students to the rapidly developing field of quantum computing, bridging physics and computer science. It aims to provide a solid theoretical foundation for understanding current research and practical applications. The course covers the gate model of quantum computation, universal gate sets, and various quantum algorithms like Shor's and Grover's. It also delves into error correction, fault-tolerant quantum computation, and the current state and architectures of quantum computers. The goal is to equip learners with the knowledge to independently analyze quantum computing literature and potentially begin practical work on quantum processors.

Curriculum

The course is structured into 12 lectures, covering fundamental concepts and advanced topics in quantum computing.

1. Course Modules
   • Introduction to Quantum Computing: Historical Perspective and Current State, The Birth of the Quantum Computing Industry. An introduction to the features of quantum computation using the simplest Deutsch algorithm.Lecture 1
   • Necessary Information from the Theory of Computational Complexity: Algorithm definition, Turing machine, universal Turing machine. Computable and non-computable functions, the halting problem. Decision problems, complexity classes. Classes P and NP. Probabilistic Turing machine, class BPP. Counting solutions, complexity class #P. The problem of demonstrating quantum supremacy using the BosonSampling problem.Lecture 2
   • Gate Model of Classical Computing, Universal Gates. Gate model of quantum computing. Elementary quantum logic gates, single-qubit and two-qubit gates. Conditional two-qubit gates, representation of conditional multi-qubit gates via two-qubit gates. Description of measurements in quantum theory, description of measurements in quantum circuits.Lecture 3
   • Universality of Single-Qubit Gates and the CNOT Gate. Discretization of single-qubit gates, universal discrete gate sets. Complexity of approximating an arbitrary unitary transformation.Lecture 4
   • 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 5
   • Algorithm for Finding the Period of a Function. Factoring numbers into prime factors, Shor's algorithm. Experimental implementations of Shor's algorithm. Other algorithms based on the quantum Fourier transform.Lecture 6
   • Quantum Search Algorithms. Grover's algorithm, geometric illustration, resource estimation. Counting the number of solutions to a search problem. Speeding up the solution of 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 7
   • Classical Error Correction Codes, Linear Codes. Errors in quantum computations, differences from the classical case. The three-qubit code correcting X-errors. The three-qubit code correcting Z-errors. Shor's nine-qubit code.Lecture 8
   • General Theory of Error Correction, Error Discretization, Independent Error Model. Classical linear codes, Hamming codes. Calderbank-Shor-Steane quantum codes.Lecture 9
   • Stabilizer Formalism, Construction of CSS Codes in Stabilizer Formalism. Unitary transformations and measurements in stabilizer formalism. Understanding fault-tolerant computation. Construction of a universal set of fault-tolerant gates. Fault-tolerant measurements. Threshold theorem. Experimental prospects for implementing quantum error correction and fault-tolerant computations.Lecture 10
   • Quantum Simulations: 'Digital' and Analog. Some experimental implementations and prospects for analog quantum simulations.Lecture 11
   • Quantum Computing on NISQ Devices. Quantum variational algorithms: QAOA and VQE. Applications to quantum chemistry problems. Implementation possibilities on modern quantum processors, development prospects.Lecture 12

Careers

Graduates of related faculties at Moscow State University are highly competitive in the job market, working in all areas where computing is applied. They find roles in academic and research institutions, government bodies, finance, consulting, and various IT companies, both domestic and international. Many also pursue further studies in postgraduate programs.

• Researcher
• Academic Staff
• Software Developer
• IT Specialist
• Data Scientist
• Quantum Computing Researcher

Frequently asked questions

What are the entry requirements for the Introduction to Quantum Computing course?

This course is primarily designed for Master's students in Physics, but senior undergraduate students in IT or Computer Engineering are also welcome. A solid understanding of linear algebra is essential, and knowledge of quantum theory mathematics is highly desirable.

How much does the Introduction to Quantum Computing course cost?

This is an online course offered through the OpenEdu platform. Specific fee structures should be checked directly on the OpenEdu website, as no tuition fees are mentioned in the provided information.

What is the format and duration of the Introduction to Quantum Computing course?

The course is delivered entirely online through video lectures and automated testing. It is structured into 12 lectures covering fundamental and advanced topics in quantum computing.

How do I apply for the Introduction to Quantum Computing course?

To enroll, visit the OpenEdu course page for 'Introduction to Quantum Computing' at Moscow State University, register or log in to your OpenEdu account, and follow the instructions to enroll.

What are the career prospects after completing this course?

Graduates from related Moscow State University faculties are competitive in various fields, including research, academia, finance, and IT. This course equips learners to analyze quantum computing literature and potentially begin practical work.