Serdecznie zapraszamy na serię wykładów poświęconych informatyce i programowaniu kwantowemu, które poprowadzi prof. Volodymyr Tkachuk z Uniwersytetu Iwana Franki we Lwowie. Prelekcje, prowadzone w języku angielskim, są skierowane głównie do studentów
i będą utrzymane na poziomie podstawowym.
Harmonogram wykładów:
10 grudnia 2024 (wtorek), godz. 12:30 (1,5 godz.) – sala 106, budynek A29
12 grudnia 2024 (czwartek), godz. 9:00 (1,5 godz.) – sala 110, budynek A29
16 grudnia 2024 (poniedziałek), godz. 10:45 (1,5 godz.) – sala 110, budynek A29
16 grudnia 2024 (poniedziałek), godz. 16:45 (1,5 godz.) – sala 110, budynek A29
Wykłady odbywają się w ramach projektu: nr RID/SP/0050/2024/1 - dofinansowanego ze środków Ministra Nauki w ramach Programu „Regionalna inicjatywa doskonałości".
W styczniu planowana jest kontynuacja spotkań.
Wszystkich serdecznie zapraszamy.
Program wykładów (Part1):
Lecture 1: Classical and quantum bit.
In this lecture, we consider classical bits, which form the foundation of classical computers, and record the simplest one-bit and two-bit classical operations. The transition from classical bits to quantum bits (qubits) is considered. The Dirac notation for describing qubit states, which serves as a foundation for quantum programming and computing, is developed.
We visualize the qubit state space using the Bloch sphere, highlighting the richness of qubit states compared to classical bits.
Operations on qubits are defined, emphasizing the importance of unitary operators associated with quantum gates. The connection between unitary operators and Hermitian operators is established.
Finally, we examine the Pauli matrices, which are Hermitian, and unitary, and serve as examples of single-qubit quantum gates.
Lecture 2: Measurement postulate. Measurement in Quantum Computing.
We explore the concept of measurement in quantum mechanics.
We formulate the postulate of measurement as the projection of a quantum system's state vector onto a chosen basis of vectors. This is precisely how measurement occurs in a quantum computer.
We introduce the concept of the arithmetic interpretation of measurement, which leads to the notion of the expectation value of an operator corresponding to a physical quantity.
Finally, we state the traditional postulate regarding the measurement of a physical quantity.
Lecture 3: Pure and mixed ensembles. Bloch sphere.
We introduce the notion of pure and mixed ensembles of states of quantum bits, which are described using a density matrix. This issue is closely related to measurements in quantum mechanics, in particular to measurements on a quantum computer. We establish the properties of the density matrix and visualize it using the Bloch sphere and the Bloch ball. Pure states belong to the Bloch sphere, and mixed states lie in the middle of the Bloch sphere and belong to the ball.
Lecture 4: Multi-qubit quantum states.
Here we consider a system of many qubits. Already two quantum bits reveal new properties that are absent for a system of two classical bits. This is the entanglement of quantum states. We introduce a measure of the entanglement of quantum states, which will allow us to determine which states are more entangled and which are less entangled. We show that the state space of a quantum bin system grows exponentially with the number of quantum bits. Therefore, modeling a system of $N$ quantum bits on a classical computer requires at least ^N$ classical bits. Note that superposition and entanglement of quantum states are an important resource in quantum computing.
Part 2 (4 Lectures) will be January.