Informação e Computação para a Inteligência Artificial! Andreas Wichert!! MEIC Tagus! (Página da cadeira: Fenix)!! Objectivo Geral! n Apresentaremos uma visão compreensiva da ciência da informação como uma parte fundamental das áreas da inteligência artificial e da computação n Exemplos na teoria da computação, que levarão às ideias de Qubits e à possível maneira de simular um computador quantum, serão fornecidos n A simulação de software com a utilização do Mathematica será realizada para o suporte à explicação das ideias por trás dos computadores quantum 1
n Organization! n Program! n Introduction! Corpo docente! n Andreas Wichert - Teóricas / Práticas! n andreas.wichert@ist.utl.pt!!! n andreas.wichert@inesc-id.pt! 2
Organização das aulas! n Teóricas:! n Matéria (slides baseados no livro e artigos e...)! n Práticas/Laboratório (weekly!):! n Exercícios! n Software Experiments! Avaliação! n Problemas praticas (Exercícios) (40%)! n +! n Exame orais (60%)! 3
Horário de dúvidas! n 2ª feira: 14H-17H (gabinete 2N5.7)! Bibliografia! n Quantum Computing, Mika Hirvensalo, Springer-Verlag, 2004! n Quantum Computing, A Gentle Introduction, Eleanor Rieffel and Wolfgang Polak, MIT Press, 2011,! n Quantum Computation and Quantum Information, Michael A. Nielsen and Isaac L.Chuang, Cambridge, 2009! 4
Bibliografia! n Quantum Computing Explained, David McMahon, 2008, Wiley Inter-Science n Howard L. Resnikoff. The Illusion of Reality. Springer-Verlag, 1987! n Colin P. Williams and Scott H. Clearwater. Explorations in Quantum Computing, Springer- Verlag 1997! Journals! n n n n L. Tarrataca and A. Wichert: Tree Search and Quantum Computation, Quantum Information Processing, 10 (4): 475-500, 2011 doi:10.1007/s11128-010-0212-z! L. Tarrataca and A. Wichert: Can Quantum Entanglement Detection Schemes Improve Search? Quantum Information Processing, in press doi:10.1007/s11128-011-0231-4! L. Tarrataca and A. Wichert: A Quantum Production Model, Quantum Information Processing, in press doi:10.1007/ s11128-011-0241-2! L. Tarrataca and A. Wichert: Problem solving and quantum computation, Cognitive Computation, in press doi:10.1007/ s12559-011-9103-6! 5
Program!! n Information theory is highly related to mathematical probability theory and thermodynamics! Reversible computation! n Bennett (1973) showed that irreversible overwriting of one bit causes energy dissipation! 6
Algorithms! n The Entscheidungsproblem is presented! n The Church-Turing thesis states that any algorithmic process can be simulated on a Turing machine.! Probability theory! n Probability theory is built around Kolmogorov's axioms! 7
Introduction to quantum Physics! n The mathematical framework of quantum theory is based on linear algebra in Hilbert space! n A 2-state quantum system is described by a two-dimensional Hilbert space. Such a 2-state quantum system corresponds to a qubit. A register is composed of several qubits and is defined by the tensor product.! Computation with Qubits! n A unitary operator on a qubit is called a unary quantum gate! n A reversible circuit can be represented by a unitary permutation matrix or by quantum Boolean gates! n The Deutsch algorithm is more powerful than any other classical algorithm! 8
Periodicy! n The discrete Fourier transform (DFT) can be seen as a linear transform represented by a unitary matrix F. This unitary matrix F also defines the quantum Fourier transform (QFT).! Search! n There is a lower bound for a quantum search on a quantum computer using a quantum oracle. The possible speedup is quadratic; NP-complete problems remain NP-complete! 9
Quantum Problem-Solving! n Using Grover's algorithm, we search through all possible paths and verify, for each path, whether it leads to the goal state! n We present the iterative quantum tree search, which is the basis of the quantum production system! Quantum cognition! n Quantum cognition uses mathematical quantum theory to model cognitive phenomena. It is assumed that the computation itself is performed on a classical computer and not on a quantum computer. The brain is considered a classical computer in a quantum world.! 10
n Questions that appear to be quite simple, such as: what are random numbers and how can we generate them, cannot be answered by traditional computer science! n Classical physics leads to the paradox of free will free will in a deterministic world! n The question concerning randomness is highly metaphysical. In classical physics, randomness does not exist! 11
What is Information? n Information first began to assume an independent and quantifiable identity in the research of physics and psychologists in the second half of the nineteenth century... n It grew in importance with the development of electrical-based communication systems 12
n Emerged as a unifying and coherent scientific concept along with the invention and development of computers n The subject matter of a science of information is abstract, for it concerns not the substance and the forces of the physical world (?) Representation n Symbolic tokens are necessarily represented by physical phenomena n thoughts are represented by the electrical and biochemical states of the neural network n There is an intermixing of the physical sciences with the proper subject matter of information science... n Information can be presented in a variety of forms which differ inessential from one another Natural language Symbols Acoustic speech Pictures 13
n Information is what remains after one abstracts from the material aspect of the physical reality... n How to do it? 14
n Scientific study of information cannot be separated from systems which are capable of bearing information n Information database and a user n Meaning - Information n Information has an independent reality, meaning does not n Meaning involves the interpretation of the information in relation to some context n Information exists n It does not need to be perceived to exist n Information = Pattern n What is a pattern? n Find measure of it... 15
The Library of Babel n The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings n Jorge Luis Borges (1899-1986) n The books contain every possible ordering of just a few basic characters (letters, spaces and punctuation marks)! n Though the majority of the books in this universe are pure gibberish, the library also must contain, somewhere, every coherent book ever written, or that might ever be written, and every possible permutation or slightly erroneous version of every one of those books! 16
n The library must contain all useful information, including predictions of the future, biographies of any person, and translations of every book in all languages! n Despite - indeed, because of -this glut of information, all books are totally useless to the reader! n Borges speculates on the existence of the "Crimson Hexagon", containing a book that contains the log of all the other books; the librarian who reads it is akin to God! 17
n The Library contains books! n Just one "authentic" volume, together with all those variants containing only a handful of misprints, would occupy so much space that they would fill the known universe! Constraints! n In a language! n Some letters are more frequent then others! n Some combination of letters are less probable! 18
History - Physics and Information n Thermodynamics is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics! n Suggestions thermodynamically descriptions are not descriptions of physical properties and relationship themselves, but of some other still more fundamental property coeval with all regimes of physical inquiry n Thermodynamically relations might remain valid for all physical theories which can describe an aspect of nature 19
n Thermodynamically quantities link physical entities to their organization, to their informational properties, and that the informational structure n Probability enter into thermodynamically considerations and opened as road for abstractions and generalization Selective Omission of Information n n Sensory data is corrupted and modified by sensing organism in ways which greatly reduce its quantity and substantially modify its original form Retaining essential information 20
What is an A?! n What makes something similar to something else (specifically what makes, for example, an uppercase letter 'A' recognisable as such)! n Metamagical Themas, Douglas Hoffstader, Basic Books, 1985! 21
Computation n The information which went into the computer is different from what came out n The most influential model of computation is the Turing Machine n The Idea of the Turing Machine grew out of on attempt to answer a question proposed by the German mathematician Hilbert in the 1900 in the International Congress of Mathematics held in Paris concerning that he be lived to be the 23 most challenging mathematical problems of the day 22
n The possibility that quantum mechanical effects might offer some thing genuinely new was first hinted by Richard Feynman of Caltech 1982 when he showed that no classical TM could cimulate certain quantum phenomena without incurring an exponential slowdown, but that a unversal quantum simulator could do so n Quantum TM has the potential for encoding many inputs to a problem simultaneously on the same tape and performing a calculation on all inputs in the time it took to do just one of the calculations classically... 23
n Quantum computers could compute certain outputs, such as true random numbers, that are not computable by any deterministic TM n There is no function that generates true random numbers n Quantum parallelsism n All the outputs are computed in the time taken to evaluate just one output classically n Unfortunately, you cannot obtain all of these outputs explicity because a measurment in the final supeposed state would only yield one output! n In principle a QTM could be used to create a proof that relied upon quantum mechanical inference among all the computations going on in superposition n Upon interrogating the QTM for an answer you might be told yes your assumption is true but there would be no way to exibit all computation steps that had gone in order to arrive at the conclusion... 24
n Organization! n Program! n Introduction! 25