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, Psychophysics, Psychophysical function
5ª aula
Uncertainty Principle for Measurement, Fourier transform, Conservation of Information, Quantum Mechanics, Conjugate pairs, Uncertainty principle, Information and Energy
6ª 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. (The pdf format was also split into three parts, so the printing is made easier)
7ª aula
Brain and Information, Crotex, Visual Cortex, Eye Movements, Information Content of Contours, Information gain in a contour
8ª aula
Invariant Pattern Recognition, Hierarchical Neural Networks, Neocognitron, Lack of intrinsic shift invariance of the Neocognitron, Delay Neocognitron
9ª aula
Associative Memory: Content-Addressable Memory; Associative Memory; Lernmatrix; Association; Heteroassociation; Learning; Retrieval; Reliability of the answer; Storage Analysis; Information Content and Information Theory, Maximizing information storage capacity, Sterling`s formula, Sparse Coding;
10ª 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
11ª aula
Overview of Quantum Computers, Qubit, Notation, Bra, Ket, Hilbert Space, Suprposition, Quantum Memory, Eigenstrates, Unitary Evolution, Observables as Hermitian Operators
12ª 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
13ª aula
Quantum States as Hilbert Space Vectors, Compound systems, Quantum Time Evolution, Observables, Spectral representation, Density Matrices
14ª aula
Unitary operators, NOT gate, square root of the not-gate, Hamarad-Walsh matrix, decomposable is entangled states, controlled not gate, No-cloning Theorem, Quantum Copymachine, Observation procedure
15ª aula
Properties of QTM, Reversible Circuits, Toffoli gate, Quantum Circuits, Spectral Representation of Unitary Operators, Rotation matrix, Unitary Evolution, Feynman’s Quantum Computer
16ª aula
Simulating a simple Quantum Computer, Feynman’s QC, Cursor Qubits, Two square rot NOT gates, Creation/Annihilation Operator, time independent Hamiltonian Operator H , Unitary Evolution Operator, Running the Quantum Computer, Measurment and Projection of the Cursor Bit, Errors in the Hamiltonian
17ª 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
18ª aula
Shor's algorithm in steps, gcd, continued fraction, continued expansion of pi , convergent to the continued fraction expansion, examples
19ª aula
Search Problems, Probabilistic Search, Randomization, Quantum Search with One Query, Quantum Blackbox, Total Probability is bigger as in Probabilistic Search
20ª 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))
21ª aula
Why can a quantum algorithm improve on NP to P?; Unitary Evolution; Deutsch-Jozsa problem; Hadamard matrix; Householder matrix; Amplitude Amplification by linear mappig; Unitary Operators: Sharp -> Superposition; Spy Systems
22ª aula
What is Teleportation? EPR effect, local interaction, nonlocal interaction, entangled state, ebit, teleporitng a qubit, we need two bits to teleport a qubit
23ª aula
No teleportation theorem, How to teleport a Qubit, Bell basis, No-communication theorem, Mach-Zehnder interferometer, IBM Test-Tube Quantum Computer , Ion Trap-Basded
24ª aula
Classical physics information , Shannon information, Von Neumann entropy, density matrix, Conjugate pairs, Heisenberg Uncertainty, Polarization, Quantum Cryptography, Detection of eavesdropping
25ª 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
