Librería Portfolio

In this book, we introduce quantum computation and its application to AI. We highlight problem solving and knowledge representation framework. Based on information theory, we cover two main principles of quantum computation ? Quantum Fourier transform and Grover search. Then, we indicate how these two principles can be applied to problem solving and finally present a general model of a quantum computer that is based on production systems.



Table of Contents:
Preface -- 1. Introduction -- 1.1. Artificial Intelligence -- 1.2. Motivation and Goals -- 1.3. Guide to the Reader -- 1.4. Content -- 1.4.1. Classical computation -- 1.4.2. Quantum computation -- 2. Computation -- 2.1. Entscheidungsproblem -- 2.1.1. Cantor´s diagonal argument -- 2.1.2. Reductio ad absurdum -- 2.2. Complexity Theory -- 2.2.1. Decision problems -- 2.2.2. P and NP -- 2.3. Church-Turing Thesis -- 2.3.1. Church-Turing-Deutsch principle -- 2.4. Computers -- 2.4.1. Analog computers -- 2.4.2. Digital computers -- 2.4.3. Von Neumann architecture -- 3. Problem Solving -- 3.1. Knowledge Representation -- 3.1.1. Rules -- 3.1.2. Logic-based operators -- 3.1.3. Frames -- 3.1.4. Categorial representation -- 3.1.5. Binary vector representation -- 3.2. Production System -- 3.2.1. Deduction systems -- 3.2.2. Reaction systems -- 3.2.3. Conflict resolution -- 3.2.4. Human problem-solving -- 3.2.5. Example -- 3.3. Sub-Symbolic Models of Problem-Solving -- 3.3.1. Proto logic -- 3.3.2. Binding problem -- 3.3.3. Icons -- 3.3.4. Euclidian geometry of the world -- 4. Information -- 4.1. Information and Thermodynamics -- 4.1.1. Dice model -- 4.1.2. Entropy -- 4.1.3. Maxwell paradox and information -- 4.1.4. Information theory -- 4.2. Hierarchical Structures -- 4.2.1. Example of a taxonomy -- 4.3. Information and Measurement -- 4.3.1. Information measure I -- 4.3.2. Nature of information measure -- 4.3.3. Measurement of angle -- 4.3.4. Information and contour -- 4.4. Information and Memory -- 4.5. Sparse code for Sub-symbols -- 4.5.1. Sparsification based on unary sub-vectors -- 4.6. Deduction Systems and Associative Memory -- 4.6.1. Taxonomic knowledge organization -- 5. Reversible Algorithms -- 5.1. Reversible Computation -- 5.2. Reversible Circuits -- 5.2.1. Boolean gates -- 5.2.2. Reversible Boolean gates -- 5.2.3. Toffoli gate -- 5.2.4. Circuit -- 6. Probability -- 6.1. Kolmogorovs Probabilities -- 6.1.1. Conditional probability -- 6.1.2. Bayes´s rule -- 6.1.3. Joint distribution -- 6.1.4. NaIve Bayes and counting -- 6.1.5. Counting and categorization -- 6.1.6. Bayesian networks -- 6.2. Mixed Distribution -- 6.3. Markov Chains -- 7. Introduction to Quantum Physics -- 7.1. Unitary Evolution -- 7.1.1. SchrOdinger´s cat paradox -- 7.1.2. Interpretations of quantum mechanics -- 7.2. Quantum Mechanics -- 7.2.1. Stochastic Markov evolution and unitary evolution -- 7.3. Hilbert Space -- 7.3.1. Spectral representation* -- 7.4. Quantum Time Evolution -- 7.5. Compound Systems -- 7.6. Von Neumann Entropy -- 7.7. Measurement -- 7.7.1. Observables -- 7.7.2. Measuring a compound system -- 7.7.3. Heisenberg´s uncertainty principle* -- 7.8. Randomness -- 7.8.1. Deterministic chaos -- 7.8.2. Kolmogorov complexity -- 7.8.3. Humans and random numbers -- 7.8.4. Randomness in quantum physics -- 8. Computation with Qubits -- 8.1. Computation with one Qubit -- 8.2. Computation with m Qubit -- 8.3. Matrix Representation of Serial and Parallel Operations -- 8.4. Entanglement -- 8.5. Quantum Boolean Circuits -- 8.6. Deutsch Algorithm -- 8.7. Deutsch Jozsa Algorithm -- 8.8. Amplitude Distribution -- 8.8.1. Cloning -- 8.8.2. Teleportation -- 8.9. Geometric Operations -- 9. Periodicity -- 9.1. Fourier Transform -- 9.2. Discrete Fourier Transform -- 9.2.1. Example -- 9.3. Quantum Fourier Transform -- 9.4. FFT -- 9.5. QFT Decomposition -- 9.5.1. QFT quantum circuit* -- 9.6. QFT Properties -- 9.7. The QFT Period Algorithm -- 9.8. Factorization -- 9.8.1. Example -- 9.9. Kitaev´s Phase Estimation Algorithm* -- 9.9.1. Order finding -- 9.10. Unitary Transforms -- 10. Search -- 10.1. Search and Quantum Oracle -- 10.2. Lower Bound ?(n) for Uf-based Search* -- 10.2.1. Lower bound of at -- 10.2.2. Upper bound of at -- 10.2.3. ?(n) -- 10.3. Grover´s Amplification -- 10.3.1. Householder reflection -- 10.3.2. Householder reflection and the mean value -- 10.3.3. Amplification -- 10.3.4. Iterative amplification -- 10.3.5. Number of iterations -- 10.3.6. Quantum counting -- 10.4. Circuit Representation -- 10.5. Speeding up the Traveling Salesman Problem -- 10.6. The Generate-and-Test Method -- 11. Quantum Problem-Solving -- 11.1. Symbols and Quantum Reality -- 11.2. Uninformed Tree Search -- 11.3. Heuristic Search -- 11.3.1. Heuristic functions -- 11.3.2. Invention of heuristic functions -- 11.3.3. Quality of heuristic -- 11.4. Quantum Tree Search -- 11.4.1. Principles of quantum tree search -- 11.4.2. Iterative quantum tree search -- 11.4.3. No constant branching factor -- 11.5. Quantum Production System -- 11.6. Tarrataca´s Quantum Production System -- 11.6.1. 3-puzzle -- 11.6.2. Extending for any n-puzzle -- 11.6.3. Pure production system -- 11.6.4. Unitary control strategy -- 11.7. A General Model of a Quantum Computer -- 11.7.1. Cognitive architecture -- 11.7.2. Representation -- 12. Quantum Cognition -- 12.1. Quantum Probability -- 12.2. Decision Making -- 12.2.1. Interference -- 12.3. Unpacking Effects -- 12.4. Conclusion -- 13. Related Approaches -- 13.1. Quantum Walk -- 13.1.1. Random walk -- 13.1.2. Quantum insect -- 13.1.3. Quantum walk on a graph -- 13.1.4. Quantum walk on one dimensional lattice -- 13.1.5. Quantum walk and search -- 13.1.6. Quantum walk for formula evaluation -- 13.2. Adiabatic Computation -- 13.2.1. Quantum annealing -- 13.3. Quantum Neural Computation -- 13.4. Epilogue -- Bibliography -- Index.