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Principles Of Quantum Artificial Intelligence: Quantum Problem Solving And Machine Learning Second Edition [Hardback]

(Univ De Lisboa, Portugal & Inesc-id, Portugal)
  • Formāts: Hardback, 496 pages
  • Izdošanas datums: 04-Aug-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811224307
  • ISBN-13: 9789811224300
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Principles Of Quantum Artificial Intelligence: Quantum Problem Solving And Machine Learning Second EditionPalielināt
  • Formāts: Hardback, 496 pages
  • Izdošanas datums: 04-Aug-2020
  • Izdevniecība: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9811224307
  • ISBN-13: 9789811224300
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9789811224300.html
Keywords:

This unique compendium presents an introduction to problem solving, information theory, statistical machine learning, stochastic methods and quantum computation. It indicates how to apply quantum computation to problem solving, machine learning and quantum-like models to decision making — the core disciplines of artificial intelligence. Most of the chapters were rewritten and extensive new materials were updated. New topics include quantum machine learning, quantum-like Bayesian networks and mind in Everett many-worlds.

Preface vii
1 Introduction
1(14)
1.1 Artificial Intelligence
1(3)
1.1.1 Machine Learning
2(2)
1.2 Motivation and Goals
4(2)
1.3 Guide to the Reader
6(1)
1.4 Content
7(8)
1.4.1 Classical computation
7(1)
1.4.2 Quantum computation
8(2)
1.4.3 Quantum machine learning
10(2)
1.4.4 Quantum-like models
12(1)
1.4.5 Quantum philosophy
13(2)
2 Computation
15(12)
2.1 Entscheidungsproblem
15(4)
2.1.1 Cantor's diagonal argument
17(1)
2.1.2 Reductio ad absurdum
18(1)
2.2 Complexity Theory
19(2)
2.2.1 Decision problems
19(1)
2.2.2 P and NP
19(2)
2.3 Church-Turing Thesis
21(1)
2.3.1 Church-Turing-Deutsch principle
21(1)
2.4 Computers
21(6)
2.4.1 Analog computers
22(1)
2.4.2 Digital computers
23(1)
2.4.3 Von Neumann architecture
24(3)
3 Problem Solving
27(18)
3.1 Knowledge Representation
27(6)
3.1.1 Rules
28(1)
3.1.2 Logic-based operators
28(3)
3.1.3 Frames
31(1)
3.1.4 Categorial representation
31(1)
3.1.5 Binary vector representation
32(1)
3.2 Production System
33(5)
3.2.1 Deduction systems
34(2)
3.2.2 Reaction systems
36(1)
3.2.3 Conflict resolution
36(1)
3.2.4 Human problem-solving
37(1)
3.2.5 Example
37(1)
3.3 Sub-Symbolic Models of Problem-Solving
38(7)
3.3.1 Proto logic
39(1)
3.3.2 Binding problem
40(1)
3.3.3 Icons
40(2)
3.3.4 Euclidian geometry of the world
42(3)
4 Information
45(38)
4.1 Information and Thermodynamics
45(10)
4.1.1 Dice model
47(1)
4.1.2 Entropy
48(1)
4.1.3 Maxwell paradox and information
49(1)
4.1.4 Information theory
50(5)
4.2 Hierarchical Structures
55(3)
4.2.1 Example of a taxonomy
57(1)
4.3 Information and Measurement
58(7)
4.3.1 Information measure I
60(3)
4.3.2 Nature of information measure
63(1)
4.3.3 Measurement of angle
63(1)
4.3.4 Information and contour
64(1)
4.4 Information and Memory
65(9)
4.5 Sparse code for Sub-symbols
74(3)
4.5.1 Sparsification based on unary sub-vectors
75(2)
4.6 Deduction Systems and Associative Memory
77(6)
4.6.1 Taxonomic knowledge organization
80(3)
5 Reversible Algorithms
83(4)
5.1 Reversible Computation
83(1)
5.2 Reversible Circuits
84(3)
5.2.1 Boolean gates
84(1)
5.2.2 Reversible Boolean gates
84(1)
5.2.3 Toffoli gate
85(1)
5.2.4 Circuit
86(1)
6 Probability
87(34)
6.1 Kolmogorovs Probabilities
87(10)
6.1.1 Conditional probability
88(1)
6.1.2 Law of total probability
89(1)
6.1.3 Bayes' rule
90(2)
6.1.4 Expectation
92(1)
6.1.5 Joint distribution
93(1)
6.1.6 Naive Bayes and counting
94(1)
6.1.7 Counting and categorization
95(2)
6.2 Bayesian Network
97(5)
6.2.1 Example
101(1)
6.3 Mixed Distribution
102(1)
6.4 Markov Chains
103(2)
6.5 Vector-Based Framework for Probabilities
105(16)
6.5.1 Vector based representation framework
108(1)
6.5.2 Conditional independence
109(2)
6.5.3 Dependency
111(1)
6.5.4 Partial dependency*
111(1)
6.5.5 Bayes' rule*
112(3)
6.5.6 Bayesian networks*
115(3)
6.5.7 Embodiment of representational framework
118(1)
6.5.8 From vector based framework to quantum physics
119(2)
7 Introduction to Quantum Physics
121(32)
7.1 Unitary Evolution
121(2)
7.1.1 Schrodinger's cat paradox
122(1)
7.1.2 Interpretations of quantum mechanics
122(1)
7.2 Quantum Mechanics
123(2)
7.2.1 Stochastic Markov evolution and unitary evolution
124(1)
7.3 Hilbert Space
125(6)
7.3.1 Spectral representation*
127(4)
7.4 Quantum Time Evolution
131(1)
7.5 Compound Systems
132(3)
7.6 Density Matrix
135(1)
7.7 Mixed states
135(1)
7.8 Shannon entropy
136(1)
7.9 Measurement
137(11)
7.9.1 Measuring a compound system
138(1)
7.9.2 Observables
139(2)
7.9.3 Expectation values
141(1)
7.9.4 Uncertainty
142(1)
7.9.5 General Heisenberg's uncertainty principle*
143(3)
7.9.6 Heisenberg's uncertainty principle*
146(1)
7.9.7 Quantum tunneling
147(1)
7.10 Observables in Quantum Computing
148(1)
7.11 Randomness
149(4)
7.11.1 Deterministic chaos
149(2)
7.11.2 Kolmogorov complexity
151(1)
7.11.3 Humans and random numbers
151(1)
7.11.4 Randomness in quantum physics
152(1)
8 Computation with Qubits
153(26)
8.1 Computation with one Qubit
153(2)
8.2 Computation with m Qubit
155(2)
8.3 Matrix Representation of Serial and Parallel Operations
157(2)
8.4 Entangelment
159(2)
8.5 Quantum Boolean Circuits
161(3)
8.6 Deutsch Algorithm
164(2)
8.7 Deutsch Jozsa Algorithm
166(3)
8.8 Amplitude Distribution
169(4)
8.8.1 Cloning
170(1)
8.8.2 Teleportation
171(2)
8.9 Geometric Operations
173(6)
9 Periodicity
179(30)
9.1 Fourier Transform
179(2)
9.2 Discrete Fourier Transform
181(3)
9.2.1 Example
183(1)
9.3 Quantum Fourier Transform
184(3)
9.4 FFT
187(1)
9.5 QFT Decomposition
188(5)
9.5.1 QFT quantum circuit*
189(4)
9.6 QFT Properties
193(2)
9.7 The QFT Period Algorithm
195(3)
9.8 Factorization
198(3)
9.8.1 Example
199(2)
9.9 Kitaev's Phase Estimation Algorithm*
201(4)
9.9.1 Order finding*
204(1)
9.10 Unitary Transforms
205(4)
10 Search
209(32)
10.1 Search and Quantum Oracle
209(2)
10.2 Lower Bound Ω(n) for Uf-based Search*
211(5)
10.2.1 Lower bound of at
212(2)
10.2.2 Upper bound of at
214(1)
10.2.3 Ω(n)
215(1)
10.3 Graver's Amplification
216(15)
10.3.1 Householder reflection
216(2)
10.3.2 Householder reflection and the mean value
218(1)
10.3.3 Amplification
219(3)
10.3.4 Iterative amplification
222(7)
10.3.5 Number of iterations
229(1)
10.3.6 Quantum counting
230(1)
10.4 Circuit Representation
231(1)
10.5 Speeding up the Traveling Salesman Problem
232(2)
10.6 The Generate-and-Test Method
234(1)
10.7 Quantum Walk
234(7)
10.7.1 Random walk
235(1)
10.7.2 Quantum insect
236(1)
10.7.3 Quantum walk on a graph
236(1)
10.7.4 Quantum walk on one dimensional lattice
237(2)
10.7.5 Quantum walk and search
239(1)
10.7.6 Quantum walk for formula evaluation
239(2)
11 Quantum Problem-Solving
241(24)
11.1 Symbols and Quantum Reality
241(1)
11.2 Uninformed Tree Search
242(3)
11.3 Heuristic Search
245(6)
11.3.1 Heuristic functions
247(1)
11.3.2 Invention of heuristic functions
248(2)
11.3.3 Quality of heuristic
250(1)
11.4 Quantum Tree Search
251(4)
11.4.1 Principles of quantum tree search
251(2)
11.4.2 Iterative quantum tree search
253(1)
11.4.3 No constant branching factor
254(1)
11.5 Quantum Production System
255(1)
11.6 Tarrataca's Quantum Production System
255(7)
11.6.1 3-puzzle
256(4)
11.6.2 Extending for any n-puzzle
260(1)
11.6.3 Pure production system
260(1)
11.6.4 Unitary control strategy
261(1)
11.7 A General Model of a Quantum Computer
262(3)
11.7.1 Cognitive architecture
263(1)
11.7.2 Representation
264(1)
12 Grover's Algorithm and the Input Problem
265(16)
12.1 Classical Input
265(1)
12.2 Quantum Binding in Context of Associative Memory
266(15)
12.2.1 Proto logic and associative memory
267(2)
12.2.2 Familiarity discrimination
269(1)
12.2.3 Visual scene coding
270(2)
12.2.4 Associations
272(1)
12.2.5 Retrieval
273(1)
12.2.6 Quantum hybrid algorithm for sub-symbolic binding
273(3)
12.2.7 Quantum oracle for familiarity discrimination
276(2)
12.2.8 Grover's iteration
278(1)
12.2.9 Cost Analysis
279(1)
12.2.10 Comparison
280(1)
13 Statistical Machine Learning
281(40)
13.1 The Karhunen-Loeve Transform
281(2)
13.1.1 Principal component analysis
283(1)
13.2 Linear Regression
283(4)
13.2.1 Design matrix
284(1)
13.2.2 Squared-error
285(1)
13.2.3 Closed-form solution
285(2)
13.3 Linear Regression and Linear Artificial Neuron
287(5)
13.3.1 Cross entropy loss function
290(2)
13.4 Multiclass Linear Discriminant
292(4)
13.4.1 Cross entropy loss function for Softmax
293(2)
13.4.2 Limitations
295(1)
13.5 Networks with Hidden Nonlinear Layers
296(4)
13.5.1 Cross entropy error function
296(1)
13.5.2 Backpropagation
297(3)
13.5.3 Computing power
300(1)
13.6 Deep Learning and Backpropagation
300(4)
13.6.1 Overrating
301(1)
13.6.2 Regularization
302(1)
13.6.3 Second and first order optimization
303(1)
13.7 Support Vector Machines
304(7)
13.7.1 Optimal hyperplane for linear separable patterns
306(1)
13.7.2 Quadratic optimization for finding the optimal hyperplane
307(2)
13.7.3 Dual problem
309(2)
13.8 Optimal Hyperplane for Non-separable Patterns
311(1)
13.8.1 Dual problem
312(1)
13.9 Support Vector Machine as a Kernel Machine
312(7)
13.9.1 Kernel trick
314(1)
13.9.2 Dual problem
315(1)
13.9.3 Classification
315(4)
13.10 Kernel Function
319(2)
13.10.1 Gaussian kernel
319(1)
13.10.2 Sigmoidal kernel
320(1)
14 Linear-Algebra Based Quantum Machine Learning
321(20)
14.1 Quantum Algorithm for Linear Systems of Equations
321(12)
14.1.1 Motivation
321(1)
14.1.2 Constraints for matrix multiplication and inversion
322(1)
14.1.3 HHL algorithm in machine learning
323(1)
14.1.4 Hamiltonian simulation
324(3)
14.1.5 Eigenvalue estimation
327(3)
14.1.6 Rotation conditioned on the eigenvalue
330(2)
14.1.7 Rotation for matrix multiplication
332(1)
14.1.8 Obtaining the solution
332(1)
14.2 Quantum Principal Component Analysis
333(2)
14.2.1 Measuring density matrix
335(1)
14.3 Quantum Random Access Memory
335(2)
14.3.1 Amplitude coding
335(2)
14.4 Quantum Kernels
337(2)
14.4.1 Swap test
337(2)
14.4.2 Quantum advantage kernels
339(1)
14.5 Problems
339(2)
15 Stochastic Methods
341(24)
15.1 Hopfield Model
341(2)
15.1.1 Storage capacity
342(1)
15.1.2 Energy function
343(1)
15.2 Ising Model
343(9)
15.2.1 Spin glass
344(1)
15.2.2 Finite temperature dynamics
344(1)
15.2.3 Boltzmann-Gibbs distribution
345(1)
15.2.4 Free energy*
346(2)
15.2.5 Stochastic dynamics
348(1)
15.2.6 Gibbs sampling
349(2)
15.2.7 Metropolis algorithm
351(1)
15.3 Simulated Annealing
352(2)
15.3.1 Combinatorial optimization
353(1)
15.4 Boltzmann Machine
354(6)
15.4.1 Stochastic dynamics of the Boltzmann machine
355(1)
15.4.2 Learning
356(2)
15.4.3 Proof of learning in Boltzmann machine*
358(2)
15.5 Harmonium - Restricted Boltzmann Machine
360(1)
15.5.1 Contrast divergence
361(1)
15.6 Deep Learning with Deep Belief Nets
361(4)
16 Adiabatic Quantum Computation and Quantum Annealing
365(20)
16.1 Adiabatic Computation
365(7)
16.1.1 Adiabatic optimization
367(3)
16.1.2 Adiabatic theorem
370(2)
16.2 Quantum Annealing
372(9)
16.2.1 Problem Hamiltonian for Ising model
373(2)
16.2.2 D-Wave
375(6)
16.3 Variational Algorithms
381(4)
16.3.1 Variational quantum eigensolvers
381(1)
16.3.2 Quantum approximate optimization algorithms
382(3)
17 Quantum Cognition
385(30)
17.1 Ordering Effects
385(2)
17.2 Quantum Probability
387(2)
17.2.1 Two-slit interference
387(2)
17.3 Decision Making
389(6)
17.3.1 Unpacking effects
394(1)
17.4 Intensity Waves
395(1)
17.5 Probability Waves
396(3)
17.5.1 Normalized probability waves
396(1)
17.5.2 Law of balance
396(3)
17.6 Balanced Probability Waves
399(8)
17.6.1 Prisoner's dilemma game and probability waves
400(2)
17.6.2 Two stage gambling game
402(2)
17.6.3 Comparison
404(2)
17.6.4 Quantum-like human decision making
406(1)
17.7 Quantum-like Bayesian Network*
407(8)
17.7.1 Probability waves sum to one according by the law of balance
408(1)
17.7.2 Probability waves are smaller equal one only after normalization
409(1)
17.7.3 Example of estimation of balanced phases
409(2)
17.7.4 Example of Bayesian network
411(4)
18 Quantum like-Evolution
415(18)
18.1 Evolutionary Dynamics
415(1)
18.2 Phase-Balanced Matrix
416(3)
18.2.1 Hadamard product
416(1)
18.2.2 Quantum law of total probability
416(3)
18.3 Quantum Like Evolution
419(7)
18.3.1 Constant phase evolution
420(1)
18.3.2 Dynamic quantum-like evolution
421(5)
18.4 Quasi Unitary Evolution*
426(7)
18.4.1 Strange oscillations*
430(3)
19 Quantum Computation and the Multiverse
433(18)
19.1 Many-worlds
433(1)
19.2 Deutsch's Decision-theoretic Argument
434(5)
19.2.1 Decision-theoretic argument
435(4)
19.3 Expected Utility and Entropy
439(6)
19.3.1 Weighted sum of surprisals
440(2)
19.3.2 Recovering probabilities from entropy
442(1)
19.3.3 Biological principle of energy minimization
443(2)
19.4 Free Will
445(1)
19.4.1 Computer metaphor
445(1)
19.4.2 Explanation as a function of the brain
446(1)
19.5 Quantum Reality
446(5)
19.5.1 Multiverse metaphor: Library of Babel metaphor
447(2)
19.5.2 Conclusion
449(2)
20 Conclusion
451(4)
20.1 Quantum Brain
451(2)
20.2 Epilogue
453(2)
Bibliography 455(18)
Index 473