Mathematical Research Seminar
Mathematical research seminar is organized by the departments of Mathematics of two members of the University - UP FAMNIT and Andrej Marušič Institute (UP IAM), every Monday from October to June.
You are cordially invited to attend the lectures.
Quantum Computers are built on the principles of Quantum Mechanics. It has been proved that many difficult problems can be solved by quantum computers. We intend to introduce quantum computing and discuss some quantum algorithms. We also intend to explore the connections between Boolean functions and quantum computing.
The topics to be discussed are as follows:
- Introduction to Quantum Mechanics and Quantum Information. Quantum States, Operators and Measurements.
- BB84: A quantum key exchange protocol.
- Quantum Entanglement. Quantum Teleportation.
- Quantum Circuits: Single qubit gates, multiple qubit gates, design of quantum circuits.
- Quantum Algorithms: Deutsch's algorithm, Deutsch's-Jozsa algorithm.
- Grover search and Its Geometric interpretation.
- Implementing quantum algorithms on IBM's quantum computer IBM-Q.
- Boolean functions and quantum computing.
In this talk I want to present the connection between the so-called cluster expansion and relation between species of graphs.
Cluster expansion is a way of dismantling highly complex correlation patterns in probability distributions describing the long term behaviour of high dimensional dynamical systems. The terms of these expansions are labeled by species of graphs, like multi-rooted simple or double connected graphs. Changing the expansion parameter is related to functional relations between the generating functions of different species.
Finally, I will discuss how one can prove convergence of theses expansion, which requires to estimate them by an expansion labeled by trees.