Μαθήματα

This is a joint course (senior undergraduate - ECE Masters program - MLDS Masters Program).

The course description is as follows:

• Brief summary of Linear Algebra concepts (vectors, planes, vector and matrix norms).
• Vectors and matrices in Matlab.
• Brief summary of functions of several variables (gradient, Hessian, level sets).
• Convex sets (definition and examples), operations on convex sets that preserve convexity.
• Convex functions (definition, examples), operations on convex functions that preserve convexity.
• Convex optimization problems (definition, examples), optimal points.
• Unconstrained optimization (characterization of optimal solution, gradient method, convergence analysis, Newton method, local convergence analysis).
• Convex optimization with constraints (Farkas Lemma, Fritz John conditions, conditions Karush-Kuhn-Tucker (KKT) - examples).
• Duality, Lagrangian, dual function, weak and strong duality – examples of dual problems.
• Convex optimization with affine equality constraints (Newton method, primal-dual).
• General convex optimization problems (barrier function, interior point method, primal-dual).
• Alternating Direction Method of Multipliers
• Introduction to distributed optimization

The Lab part of the course consists of four (4) projects which contain theoretical questions as well as matlab (or octave) code implementing selected optimization algorithms.

Grading;

• Final Exam 6/10,
• Projects (4/10).

Our main source will be the textbook

S. Boyd and L. Vandenberghe. "Convex Optimization," Cambridge University Press, 2004 (I uploaded the textbook in the "Εγγραφα" section).

See also the video series of recent Boy's lectures 

https://www.youtube.com/playlist?list=PLoROMvodv4rMJqxxviPa4AmDClvcbHi6h

Another excellent source is the book

A. Beck, Introduction to nonlinear optimization (2nd edition), SIAM.

Fundamentals of programming with Python and Python libraries for data manipulation. This is a hands-on course with a substantial amount of project work. No prior knowledge of Python is needed, but a basic understanding of programming concepts (variables, types, functions, files, etc) as well as computer use skills are required.

• Part I: We will cover principles of object-oriented and structured programming, data representation via Python data structures, and fundamental data manipulation in idiomatic Python. Then, we will examine Python libraries for scientific computing (numpy and scipy).
• Part II: We will learn to work with basic software development technologies (version control, package installation, package publication) and interactive environments. A practical introduction to Jupyter, pandas, scikit-learn and matplotlib will be followed by students demonstrating their use on introductory data analysis tasks.
• Part III: An introduction to high-performance computing techniques via Python, including dask and tensorflow will be given. Students will be asked to implement all stages of a scientific workflow, demonstrating the skills acquired in the previous stages of the course.

Requirements: basic knowledge of programming in any programming language

Probability spaces, Random Variables and Stochastic Processes, Conditional Probability, Expected Values, Conditional Expectations, Independence of Random Variables. The Bernoulli Stochastic Process and Sums of Independent Random Variables: Bernoulli Process, Number of Successes, Times of Successes, Sums of Independent Random Variables, Chebyshev Inequality, Weak and Strong Law of Large Numbers, Central Limit Theorem.
Basics of Inference and Testing (including maximum likelihood estimates, hypothesis testing, likelihood ratio test, and Bayesian inference), Linear regression models, Generalized linear regression models (including logistic regression), Nonparametric Regression (including Gaussian Process regression), Tree methods and Forests, Bagging and Ensemble methods, Statistical Computing.

Το μάθημα δεν διαθέτει περιγραφή

State vector Hilbert spaces, Qubit. Theory of quantum measurements, orthonormal complete bases, projectors, positive operator-valued probability measures (POVM). Density matrix, spectral decomposition, convex decomposition. Bloch sphere and vector. Introduction to quantum entanglement. Quantum correlations, Biorthogonal analysis, Schmidt numbers. Measures of entanglement, Quantum entropy measures. Quantum information. The Schroedinger–HJW theorem. Quantum channels (single qubit, collective channels). Quantum algorithms, Computational and communicational algorithms. The Deutsch–Jozsa algorithm. Quantum teleportation algorithm for states, gates, channels. The LOCC protocol. Quantum walks (QW). Coin-walker Hilbert spaces. The QW channel maps. Quadratic speed ups. Introduction to the Helstrom-Holevo quantum estimation theory. Cramer-Rao bound and quantum Fisher information. Optimal measurements and the symmetric logarithmic derivative operator. Phase estimation problems of quantum states. Temperature estimation and qubit thermometry for closed and open quantum systems.

Χώροι Hilbert καταστατικών διανυσμάτων - Qubit. Θεωρία κβαντικών μετρήσεων, ορθοκανονικές βάσεις, προβολικοί τελεστές. Θετικά τελεστικά μέτρα πιθανότητας POVM. Πίνακας πυκνότητας, φασματική ανάλυση, κυρτοί συνδυασμοί. Σφαίρα κα διάνυσμα Bloch. Εισαγωγή στο κβαντικό εναγκαλισμό. Κβαντικές συσχετίσεις - Διορθογώνια ανάλυση - Αριθμοί Schmidt. Μετρήσεις εναγκαλισμού- Μέτρα κβαντικής εντροπίας. Κβαντική Πληροφορία. Το θεώρημα Schroedinger -HJW. Κβαντικά κανάλια (1-qubit, συλλογικά κανάλια). Κβαντικοί αλγόριθμοι - Αλγόριθμοι υπολογισμών και επικοινωνίας. Ο αλγόριθμος Deutsch--Jozsa. Κβαντική τηλεμεταφορά καταστάσεων, πυλών, καναλιών. Το πρωτόκολο LOCC. Κβαντικοί περίπατοι (QW). Χώροι Hilbert νομίσματος-περιπατητή. Κανάλια τύπου QW. Τετραγωνικές επιταχύνσεις. Εισαγωγή στη θεωρία κβαντικής εκτιμητικής Helstrom-Holevo. Φράγμα Cramér-Rao και κβαντική πληροφορία Fisher. Βέλτιστες μετρήσεις και ο συμμετρικός τελεστής λογαριθμικής παραγώγου. Προβλήματα εκτιμητικής γωνίας φάσης σε κβαντικές καταστάσεις. Εκτιμητική θερμοκρασίας και θερμιδομετρία  qubit για κλειστά και ανοιχτά κβαντικά συστήματα.

 Photo: https://en.wikipedia.org/wiki/One-way_quantum_computer#/media/File:Bernstein_Vazirani_quantum_circuit.png

Διαλέξεις/Lectures

Πέμπτη/Thu,           12:00-13:00  αιθ./Classroom 2041
Παρασκευή/Fri,      12:00-15:00 αιθ.Classroom 2041

Ώρες γραφείου :   Μία ώρα μετά το τέλος των διαλέξεων Πέμπτης και Παρασκευής ή μετά από συνεννόηση