1ª aula

Apresentação: Organization, Program, Introduction

1ª aula

Apresentação: Organization, Program, Introduction

2ª aula

Thermodynamics, Entropy, Macroscoping and Microscoping state, Dice model , Information and Entropy, Definition of Entropy as the number of Questions

3ª aula

Communication, Message, Information Theory, Representation of information, Signal alphabet, Surprise, Information and probability, Statistical encoding, Entropy of Images

4ª aula

What are numbers, Information Content of a Measurement, Gain of Information, Information gain in a contour

5ª aula

Hierarchical Organization, Trees, How many nodes should each level contain in order that the average waiting time required is as small as possible? DNA Numbers and Ontologies, Hierarchical Subspaces, Optimal number of Hierarchical Subspaces.

6ª aula

Brain and Information, Crotex, Visual Cortex, Eye Movements,Invariant Pattern Recognition, Hierarchical Neural Networks, Neocognitron, Lack of intrinsic shift invariance of the Neocognitron, Associative Memory: Content-Addressable Memory; Associative Memory; Lernmatrix; Association; Heteroassociation; Learning; Retrieval; Reliability of the answer; 

7ª aula

Aula by João Sacramento: Associative memory, Storage Analysis (according to Palm); Information Content and Information Theory, Maximizing information storage capacity

8ª aula

Entscheidungsproblem, Turing machine, Halting Problem, Godel, Computability, Univerality, Complexity, Church-Turing thesis, Strong Church-Turing thesis, Reformulation of the Strong Church-Turing thesis by Deutsch, Probabilistic Turing Machine, Quantum Turing Machine, Reversible gates

9ª aula

Overview of Quantum Computers, Qubit, Notation, Bra, Ket, Hilbert Space, Suprposition, Quantum Memory, Eigenstrates, Unitary Evolution, Observables as Hermitian Operators

10ª aula

Classical Physics, Hamiltonian equation of motion, Probabilistic System, Markov chain, Quantum coin, destructive interference, Hilbert Spaces, Operators, adjoint operator,self-adjoint operator, unitary operator, Spectral representation, Spectral Representation of Unitary Operators



11ª aula

Quantum States as Hilbert Space Vectors, Compound systems, Quantum Time Evolution, Observables, Spectral representation, Density Matrices

12ª aula

Unitary operators, NOT gate, square root of the not-gate, Hamarad-Walsh matrix, decomposable is entangled states, controlled not gate

13ª aula

No-cloning Theorem, Quantum Copymachine, Observation procedure, Properties of QTM, Reversible Circuits, Toffoli gate, Quantum Circuits

14ª aula

Hadamard Gates, Matrix representation of serial and parallel operations, Deutsch Algorithm, Deutsch-Jozsa Algorithm

15ª aula

Deutsch Algorithm, review, what is Deutsch Jozsa Algorithm? (Lecture was given on the blackboard)

16ª aula

Search Problems, Probabilistic Search, Randomization, Quantum Search with One Query, Quantum Blackbox, Total Probability is bigger as in Probabilistic Search (Lecture given on blackboard)

17ª aula

Operators for Grover's Amplification, Amplitude Amplification, inversion about average, probability to find the answer, Iterative use, what is the requiered number of queries?, NP problems and the complexity O(sqrt(2**n))

18ª aula

Iterative use, what is the requiered number of queries? (Lecture given on blackboard)

19ª aula

Symmetric Cryptography, Asymmetric Cryptography, RSA, Number Field Sieve" heuristic algorithm, Code-Breaking on a Quantum Computer, Shor's Algorithm, period of x modulo n, quantum algorithm, discrete fourier transform, simulation, gcd, continued fraction, continued expansion of pi , convergent to the continued fraction expansion, examples

20ª aula

Characters of Abelian Group, Dual Group, Orthogonality of the Characters, Discrete Fourier Transform, Quantum Fourier Transform, Hadarmad-Walsh Transform, Finding Period, Example (Lecture on Blackboard)

21ª aula

Number Theory: Euclid's Algorithm, Continous Fraction (Given Blackboard)

How to make a Quantum Computer:  Mach-Zehnder interferometer, IBM Test-Tube Quantum Computer , Ion Trap-Basded (Slides)

22ª aula

What is Teleportation? EPR effect, local interaction, nonlocal interaction, entangled state, ebit, teleporitng a qubit

23ª aula

Classical physics information , Shannon information, Von Neumann entropy, density matrix, Conjugate pairs, Heisenberg Uncertainty, Polarization, Quantum Cryptography, Detection of eavesdropping

24ª aula

Overview: The Library of Babel, What is an A?, Entropy - Information, Measurment, Hierarchy, Information Gain, Neocognitron, Associative Memory, Entscheidungsproblem, The Church-Turing thesis, Simple 2-state system, qubit, Compound systems, Toffoli gate, Spectral Representation of Unitary Operators, Shor's Algorithm for factoring n, Grover's Amplification, No teleportation theorem, ebit, von Neumann entropy, Heisenberg Uncertainty