“Introduction to Quantum Computing” - course RUB 2,800. from MSU, training 15 weeks. (4 months), Date: November 30, 2023.

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. Necessary information from the theory of computational complexity of algorithms. 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. Gate model of classical computing, universal gates. 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. The versatility of single-qubit gates and the CNOT gate. 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. Algorithm for finding the period of a function. 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. Classic error correction codes, linear 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. General theory of error correction, error sampling, independent error model. Classical linear codes, Hamming codes. Quantum Calderbank-Shor-Steen codes.

Lecture 10. 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 on NISQ devices. 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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