A Practical Guide to Quantum Machine Learning and Quantum Optimization: Hands-on Approach to Modern Quantum Algorithms

Preface
 I I, for One, Welcome our New Quantum Overlords
 1 Foundations of Quantum Computing
 1.1 Quantum computing: the big picture
 1.2 The basics of the quantum circuit model
 1.3 Working with one qubit and the Bloch sphere
 1.3.1 What is a qubit?
 1.3.2 Dirac notation and inner products
 1.3.3 One-qubit quantum gates
 1.3.4 The Bloch sphere and rotations
 1.3.5 Hello, quantum world!
 1.4 Working with two qubits and entanglement
 1.4.1 Two-qubit states
 1.4.2 Two-qubit gates: tensor products
 1.4.3 The CNOT gate
 1.4.4 Entanglement
 1.4.5 The no-cloning theorem
 1.4.6 Controlled gates
 1.4.7 Hello, entangled world!
 1.5 Working with multiple qubits and universality
 1.5.1 Multi-qubit systems
 1.5.2 Multi-qubit gates
 1.5.3 Universal gates in quantum computing
 Summary
 2 The Tools of the Trade in Quantum Computing
 2.1 Tools for quantum computing: a non-exhaustive overview
 2.1.1 A non-exhaustive survey of frameworks and platforms
 2.1.2 Qiskit, PennyLane, and Ocean
 2.2 Working with Qiskit
 2.2.1 An overview of the Qiskit framework
 2.2.2 Using Qiskit Terra to build quantum circuits
 2.2.3 Using Qiskit Aer to simulate quantum circuits
 2.2.4 Let’s get real: using IBM Quantum
 2.3 Working with PennyLane
 2.3.1 Circuit engineering 101
 2.3.2 PennyLane’s interoperability
Summary
 II When Time is Gold: Tools for Quantum Optimization
 3 Working with Quadratic Unconstrained Binary Optimization Problems
 3.1 The Max-Cut problem and the Ising model
 3.1.1 Graphs and cuts
 3.1.2 Formulating the problem
 3.1.3 The Ising model
 3.2 Enter quantum: formulating optimization problems the quantum way
 3.2.1 From classical variables to qubits
 3.2.2 Computing expectation values with Qiskit
 3.3 Moving from Ising to QUBO and back
 3.4 Combinatorial optimization problems with the QUBO model
 3.4.1 Binary linear programming
 3.4.2 The Knapsack problem
 3.4.3 Graph coloring
 3.4.4 The Traveling Salesperson Problem
 3.4.5 Other problems and other formulations
 Summary
 4 Adiabatic Quantum Computing and Quantum Annealing
 4.1 Adiabatic quantum computing
 4.2 Quantum annealing
 4.3 Using Ocean to formulate and transform optimization problems
 4.3.1 Constrained quadratic models in Ocean
 4.3.2 Solving constrained quadratic models with dimod
 4.3.3 Running constrained problems on quantum annealers
 4.4 Solving optimization problems on quantum annealers with Leap
 4.4.1 The Leap annealers
 4.4.2 Embeddings and annealer topologies
 4.4.3 Controlling annealing parameters
 4.4.4 The importance of coupling strengths
 4.4.5 Classical and hybrid samplers
 Summary
 5 QAOA: Quantum Approximate Optimization Algorithm
 5.1 From adiabatic computing to QAOA
 5.1.1 Discretizing adiabatic quantum computing
 5.1.2 QAOA: The algorithm
 5.1.3 Circuits for QAOA
5.1.4 Estimating the energy
 5.1.5 QUBO and HOBO
 5.2 Using QAOA with Qiskit
 5.2.1 Using QAOA with Hamiltonians
 5.2.2 Solving QUBO problems with QAOA in Qiskit
 5.3 Using QAOA with PennyLane
 Summary
 6 GAS: Grover Adaptive Search
 6.1 Grover’s algorithm
 6.1.1 Quantum oracles
 6.1.2 Grover’s circuits
 6.1.3 Probability of finding a marked element
 6.1.4 Finding minima with Grover’s algorithm
 6.2 Quantum oracles for combinatorial optimization
 6.2.1 The quantum Fourier transform
 6.2.2 Encoding and adding integer numbers
 6.2.3 Computing the whole polynomial
 6.2.4 Constructing the oracle
 6.3 Using GAS with Qiskit
 Summary
 7 VQE: Variational Quantum Eigensolver
 7.1 Hamiltonians, observables, and their expectation values
 7.1.1 Observables
 7.1.2 Estimating the expectation values of observables
 7.2 Introducing VQE
 7.2.1 Getting excited with VQE
 7.3 Using VQE with Qiskit
 7.3.1 Defining a molecular problem in Qiskit
 7.3.2 Using VQE with Hamiltonians
 7.3.3 Finding excited states with Qiskit
 7.3.4 Using VQE with molecular problems
 7.3.5 Simulations with noise
 7.3.6 Running VQE on quantum computers
 7.3.7 The shape of things to come: the future of Qiskit
 7.4 Using VQE with PennyLane
 7.4.1 Defining a molecular problem in PennyLane
 7.4.2 Implementing and running VQE
 7.4.3 Running VQE on real quantum devices
 Summary