Quantum Computing

Objectives and outcomes
The aim of this course is to provide students with a basic knowledge of quantum computing. The most important quantum programs and their applications to well-known quantum algorithms are covered, with performance comparisons with classical computing. Upon completion of this course, students will be able to use mathematical tools to predict the results of quantum logic circuits, explain and analyse quantum algorithms described in quantum computing models based on quantum circuits and measurement, discuss the difference in performance between classical and quantum computers and critically study and understand the scientific literature on quantum computing.

Lectures
Linear algebra necessary to understand quantum mechanics. Vector spaces. Inner product, Hilbert space and Dirac notation. Basis, canonical basis and diagonal state. The Bloch sphere and the concept of the qubit. Linear operators, Pauli matrices, the tensor product, qubit registers. Quantum systems, superposition, entanglement and measurements. Quantum computing using quantum logic circuits. Description of the universal set of logic circuits. Quantum teleportation and superdense coding. Quantum programs (return phase, quantum Fourier transform, phase estimation). Quantum algorithms: Grover, Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon and Shor. Quantum computations using a model based on measurements. Graph-state description and the mathematics of measurement. Quantum coding and error correction. Quantum computing with big data. Applications in drug design, chemistry, biology, materials science, cryptography, finance.

Practical classes
Becoming familiar with the tools for programming the quantum computer IBM Quantum (Quantum services, Quantum Composer, Quantum Lab). Bits, qubits and operations with them. Basic quantum logic circuits (gates). Multi-qubit gates. Measuring gates and the Born rule. Connecting gates to a circuit and testing it using IBM-QX Composer. The process of quantum computing with simple examples. Working with QISKit Terra SDK environment. Microsoft Q#, Quantum Development Kit and Azure Quantum. Examples of executing some quantum algorithms on a simulator and on a real quantum computer.