Quantum Artificial Intelligence with Qiskit

✍ Scribed by Andreas Wichert

• Publisher: CRC Press
• Year: 2023
• Tongue: English
• Leaves: 326
• Category: Library

✦ Synopsis

Quantum Artificial Intelligence (QAI) is a new interdisciplinary research field that combines quantum computing with Artificial Intelligence (AI), aiming to use the unique properties of quantum computers to enhance the capabilities of AI systems. This book provides a cohesive overview of the field of QAI, providing the tools for readers to create and manipulate quantum programs on devices as accessible as a laptop computer.

Introducing symbolical quantum algorithms, sub symbolical quantum algorithms and quantum Machine Learning (ML) algorithms, this book explains each process step-by-step with associated QISKIT listings. All examples are additionally available for download athttps://github.com/andrzejwichert/qai.

Allowing readers to learn the basic concepts of quantum computing on their home computer, this book is accessible both the general readership as well as students and instructors of courses relating to computer science and artificial intelligence.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Author
CHAPTER 1: Artificial Intelligence
1.1. A SHORT HISTORY OF AI
1.1.1. Cybernetics
1.1.2. Symbolic Artificial Intelligence
1.1.3. Connectionist Movement
1.1.4. Deep Learning
1.1.5. Quantum Artificial Intelligence
1.2. SYMBOLICAL ARTIFICIAL INTELLIGENCE
1.2.1. Bits
1.2.2. Rules and Operators
1.2.3. Production Systems
1.2.4. Tree Search
1.2.5. Informed Tree Search
1.3. MACHINE LEARNING
1.3.1. Vector Representation
1.3.2. Nearest Neighbor
1.3.3. Associative Memory
1.3.4. Artificial Neuron
1.3.5. Perceptron
1.3.6. Support Vector Machine
1.3.7. Support Vector Machine as a Kernel Machine
1.3.8. Deep Learning
CHAPTER 2: Quantum Physics and Quantum Computation
2.1. QUANTUM MEASUREMENT
2.1.1. Interpretations of Quantum Mechanics
2.2. PRINCIPLES OF QUANTUM COMPUTATION
2.2.1. Qubits
2.2.2. Representation
2.2.3. Linear Operators
2.3. COMPOUND SYSTEMS
2.4. MEASUREMENT
2.5. COMPUTATION WITH ONE QUBIT
2.6. COMPUTATION WITH M QUBIT
2.6.1. Matrix Representation of Serial and Parallel Operations
2.7. ENTANGLEMENT
2.8. CLONING
2.9. PHASE KICK-BACK
2.10. QUANTUM BOOLEAN GATES
CHAPTER 3: Qiskit
3.1. SOFTWARE DEVELOPMENT KIT
3.2. INSTALLATION
3.3. BACKEND SIMULATOR FUNCTIONS
3.4. COMPATIBILITY
3.5. EXAMPLE: QUANTUM COIN
3.5.1. Statevector Evaluation
3.5.2. Qasm Simulator Evaluation
3.6. MATRIX REPRESENTATION
3.7. QUANTUM CIRCUITS
3.7.1. Un-computing
3.7.2. General Multi-Controlled X Gate
3.7.3. OR Operation
3.8. DEUTSCH ALGORITHM
3.9. DEUTSCH ALGORITHM ON A REAL QUANTUM COMPUTER
CHAPTER 4: Quantum Gates
4.1. BOOLEAN ALGEBRA AND THE QUANTUM GATES
4.1.1. Identity Gate – I
4.1.2. NOT Gate, Pauli X Gate – X
4.1.3. Toffoli Gate – ccX
4.1.4. Controlled NOT Gate – cX
4.1.5. SWAP Gate – SWAP
4.1.6. Controlled SWAP Gate – cS
4.2. GATES FOR ONE QUBIT
4.2.1. Clifford Gates for One Qubit
4.2.2. Pauli Y Gate – Y
4.2.3. Pauli Z Gate – Z
4.2.4. S Gate – S
4.2.5. Sdag Gate – S†
4.3. ROTATION GATES
4.3.1. T Gate – T
4.3.2. T† Gate – T†
4.4. PARAMETERIZED ROTATION GATES
4.4.1. RX Gate – RX
4.4.2. RY Gate – RY
4.4.3. RZ Gate – RZ
4.4.4. U Gate – U
4.4.5. Phase Gate – P
4.5. CONTROLLED U GATES
4.5.1. Controlled Phase Gate
4.5.2. Controlled Hadamard Gate – cH
4.6. UNIVERSALITY
4.7. QUANTUM CIRCUITS
CHAPTER 5: Grover’s Amplification
5.1. SEARCH AND QUANTUM ORACLE
5.1.1. Quantum Oracle
5.2. HOUSEHOLDER REFLECTION
5.3. GROVER’S AMPLIFICATION
5.3.1. Number of Iteration
5.3.2. Circuit Representation
5.4. NUMPY EXAMPLE WITH MATRIX NOTATION
5.5. DECOMPOSITION
5.6. QISKIT EXAMPLES
5.7. UN-COMPUTATION
5.8. GENERALIZATION OF ΛM FOR M QUBITS
CHAPTER 6: SAT Problem
6.1. FORMULA SATISFIABILITY
6.2. SAT PROBLEM AND NP COMPLETE
6.3. SAT PROBLEM AND GROVER’S ALGORITHM
6.3.1. Quantum Boolean Circuit
6.3.2. Un-Computation
6.3.3. Grover’s Amplification
6.3.4. No Solution
CHAPTER 7: Symbolic State Representation
7.1. BIT REPRESENTATION OF OBJECTS AND ATTRIBUTES
7.1.1. “What” and “Where”
7.2. TREE SEARCH AND THE PATH DESCRIPTORS
7.3. QUANTUM TREE SEARCH
CHAPTER 8: Quantum Production System
8.1. PURE PRODUCTION SYSTEMS
8.1.1. Quantum Production Systems
8.2. EXAMPLE: SORTING A STRING
8.2.1. Quantum Production System for Sorting a String
8.2.2. Number of Iteration
8.3. COGNITIVE ARCHITECTURE
8.4. CONTROL FUNCTION
CHAPTER 9: 3 Puzzle
9.1. 3 PUZZLE
9.2. REPRESENTATION
9.2.1. Rules and Trace
9.3. SEARCH OF DEPTH TWO
9.4. SEARCH DEPTH THREE
9.5. SEARCH DEPTH THREE WITH TWO ITERATIONS
CHAPTER 10: 8 Puzzle
10.1. REPRESENTATION
10.2. NUMBER OF ITERATIONS
CHAPTER 11: Blocks World
11.1. REPRESENTATION
11.1.1. Rules (Productions)
11.1.2. Oracle
11.1.3. Architecture
11.2. EXAMPLES
11.3. NUMBER OF ITERATIONS
CHAPTER 12: Five Pennies Nim Game
12.1. QUANTUM CIRCUIT
12.1.1. Representation of Rules
12.1.2. Oracle
12.1.3. Search of Depth Two
12.2. LIMITATIONS OF QUANTUM TREE SEARCH
CHAPTER 13: Basis Encoding of Binary Vectors
13.1. BINARY VECTORS
13.2. SUPERPOSITIONS OF BINARY PATTERNS
13.2.1. Storage Algorithm
13.2.2. Qiskit Example
13.3. ENTANGLEMENT OF BINARY PATTERNS
13.3.1. Qiskit Example
13.4. COMPARISON
CHAPTER 14: Quantum Associative Memory
14.1. QUANTUM NEAREST NEIGHBOR
14.2. QUANTUM ASSOCIATIVE MEMORY (QuAM)
14.2.1. Non-Uniform Distribution
14.2.2. Ventura Martinez Trick
14.3. INPUT DESTRUCTION PROBLEM
CHAPTER 15: Quantum Lernmatrix
15.1. LERNMATRIX
15.1.1. Learning and Retrieval
15.1.2. Storage Capacity
15.2. MONTE CARLO LERNMATRIX
15.3. QUANTUM COUNTING ONES
15.4. QUANTUM LERNMATRIX
15.4.1. Generalization
15.4.2. Example
15.4.3. Applying Trugenberger Amplification Several Times
15.4.4. Tree-Like Structures
15.5. CONCLUSION
CHAPTER 16: Amplitude Encoding
16.1. AMPLITUDE ENCODING EXAMPLE
16.2. TOP-DOWN DIVIDE STRATEGY
16.2.1. Level 1
16.2.2. Level 2
16.2.3. Level 3
16.3. COMBINING STATES
16.3.1. Level 2
16.3.2. Level 3
16.4. QISKIT AMPLITUDE CODING
16.5. SWAP TEST
16.5.1. Example for Two-Dimensional Vectors
16.5.2. Example for Four-Dimensional Vectors
CHAPTER 17: Quantum Kernels
17.1. QUANTUM KERNELS
17.2. QUANTUM KERNELS AND SWAP TEST
17.2.1. Example for Two-Dimensional Vectors
17.3. QUANTUM KERNELS AND INVERSION TEST
17.3.1. Example
17.3.2. Quantum Feature Maps
17.4. QUANTUM SUPPORT VECTOR MACHINE
CHAPTER 18: qRAM
18.1. QUANTUM RANDOM ACCESS MEMORY
18.1.1. The Bucket Brigade Architecture of qRAM
18.1.2. Amplitude Coding
CHAPTER 19: Quantum Fourier Transform
19.1. DISCRETE FOURIER TRANSFORM
19.2. QUANTUM FOURIER TRANSFORM
19.3. QFT DECOMPOSITION
19.3.1. QFT for Two qubits
19.3.2. QFT for Three qubits
19.3.3. QFT for Four qubits
19.3.4. QFT Costs
19.3.5. QFT
CHAPTER 20: Phase Estimation
20.1. KITAEV’S PHASE ESTIMATION ALGORITHM
20.1.1. Example with T Gate
20.2. QUANTUM COUNTING
20.2.1. Example
CHAPTER 21: Quantum Perceptron
21.1. COUNTING OF ONES WITH KITAEV’S PHASE ESTIMATION ALGORITHM
21.2. QUANTUM PERCEPTRON
21.3. SIMPLE EXAMPLE
CHAPTER 22: HHL
22.1. QUANTUM ALGORITHM FOR LINEAR SYSTEMS OF EQUATIONS
22.2. ALGORITHM
22.2.1. Hamiltonian Simulation
22.2.2. Kitaev’s Phase Estimation
22.2.3. Conditioned Rotation
22.2.4. Un-Computation
22.2.5. Measurement
22.2.6. Obtaining the Solution
22.3. EXAMPLE
22.3.1. Kitaev’s Phase Estimation to Hamiltonian Simulation
22.3.2. Conditioned Rotation and Un-Computation
22.3.3. Obtaining the Solution
22.4. CONSTRAINTS
CHAPTER 23: Hybrid Approaches − Variational Classification
23.1. VARIATIONAL CLASSIFICATION
23.1.1. Example
23.2. CROSS ENTROPY LOSS FUNCTION
23.2.1. Multi-Class Loss Function
23.3. SPSA OPTIMIZER
23.3.1. Qiskit Variational Quantum Classifier
CHAPTER 24: Conclusion
24.1. EPILOGUE
24.2. FURTHER READING
Bibliography
Index