Quantum Computing by Practice: Python Programming in the Cloud with Qiskit and IBM-Q

Table of Contents
About the Author
About the Technical Reviewer
Introduction
Chapter 1: Quantum Fields: The Building Blocks of Reality
	Enter Max Planck, the Father of Quantum Mechanics
	Planck Hits the Jackpot, Einstein Collects a Nobel Prize
		The Nature of Light Before Planck
		After Planck, Physics Will Never Be the Same
	Quantum Mechanics Comes in Many Flavors
		Copenhagen Interpretation
			The Revolution Begins with Planck, Bohr, and Schrödinger
			The Genius of Paul Dirac
			Einstein vs. Bohr, Nonlocality and Spooky Action at a Distance (EPR Paradox)
			Bell’s Theorem Settles Einstein vs. Bohr and the EPR Paradox
			Consciousness, Mysticism, and the Collapse of the Wave Function
		Many Worlds Interpretation
		Supplementary Interpretations
			Conscious Observer
			Quantum Information
			Pilot Wave Theory
			Time-Symmetric Theories
			De-coherence
	From Quantum Mechanics to Quantum Fields: Evolution or Revolution
		We Are All Made of Quantum Fields, but We Don’t Understand Them
		The Recipe to Build a Universe
		The Fantastic Four Forces of Nature: Enter the Higgs Field
		Standard Model and the Super-Equation of Physics
		Chasing the Unexplained
		Dark Energy Will Determine the Ultimate Fate of the Universe
		Beyond the Standard Model
			LHC Is Back with a Vengeance
			Grand Unification and Supersymmetry: The Holy Grail of Physics
			Doom and Gloom in the Horizon
			When We Are Wrong, We Start to Make Progress
	Exercises
Chapter 2: Richard Feynman, Demigod of Physics, Father of the Quantum Computer
	Mysteries of QFT: The Plague on Infinities
		Electron Scattering According to QED
		Perturbation Theory: If You Can’t Do Something Perfectly, Maybe Near Enough Is Good Enough
		Tackling Those Pesky Infinities with Renormalization
		Renormalization: Electrons Do Not Have Infinite Mass
		QFT’s Holy Trinity: Perturbation Theory, Renormalization, and Feynman Diagrams
	Feynman Diagrams: Formulas in Disguise
		Feynman Approach to Quantum Mechanics: The Path Integral
		Unraveling the Impossible: Feynman Diagrams to the Rescue
		A Few Simple Diagram Rules Are All That Is Needed
		The Strangeness of Virtual Particles
		The Power of Feynman Diagrams to Simplify QFT-QED Calculations
	Antimatter As Time Reverse Matter and the Mirror Universe
		The Foundations of Quantum Theory Rest on Symmetries
		Broken Symmetries Threaten to Break All of Physics Along with Them
			Can CP Symmetry Be Saved by a Clock?
			Strike 2: CP Symmetry Is Violated, Three Strikes, and Physics Is Ruined
			Time Symmetry Conservation: The Hallowed CPT Looks in Danger
		Particles in a Rewinding Universe
		CPT Is Safe: The 70-Year Rollercoaster Ride for the Symmetries of Nature
	Exercises
Chapter 3: Behold, the Qubit Revolution
	Your Friendly Neighborhood Quantum Computer
		Two-Photon Quantum Interference
		Mathematics Behind Photonic Interference
		Output States of the Control-Z Gate
		Lowering Error Rates
	Superconducting Loops vs. Linear Optics
		Superconducting Loops
		Breaking Out of the Lab: IBM-Q Qubit Design
			Qubit Signal Amplifier
			Microwave and Superconducting Coaxial Lines
			Cryogenic Insulators and Shields
			The Non-destructible Way of Reading the Quantum State of a Qubit
		Pros and Cons of Superconductor Loops
	The Many Flavors of the Qubit
	Exercises
Chapter 4: Enter IBM Quantum: A One-of-a-Kind Platform for Quantum Computing in the Cloud
	Getting Your Feet Wet with IBM Quantum
		Quantum composer
		Quantum Gates
		Quantum Backends Available for Use
	Entanglement: Bell and GHZ States
		Two Qubit Entanglement with Bell States
		Three Qubit Entanglement with GHZ States Tests
		Super Determinism: A Way Out of the Spookiness. Was Einstein Right All Along?
	Remote Access via the REST API
		Authentication
			Authentication via API Token
			Authentication via User-Password
		List Available Backends
			Request Parameters
			HTTP Headers
			Response Sample
		Get Backend Parameters
			Request Parameters
			HTTP Headers
			Response Sample
		Get the Status of a Processor’s Queue
			Request Parameters
			HTTP Headers
			Response Sample
		List Jobs in the Execution Queue
			Request Parameters
			HTTP Headers
			Response Sample
		Get Account Information
			Request Parameters
			HTTP Headers
			Response Sample
		List User’s Experiments
			Request Parameters
			HTTP Headers
			Response Sample
		Run a Job on Hardware
			HTTP Headers
			Payload Format
			Response Format
		Get the API Version
			Request Parameters
			HTTP Headers
			Response Format
	Exercises
Chapter 5: Mathematical Foundation: Time to Dust Up That Linear Algebra
	Qubit 101: Vector, Matrices, and Complex Numbers
		Transpose of a Matrix MT
		Conjugate Transpose or Adjoint Mϯ
		Complex Numbers: The Mathematical Magic Hats
	Euler’s Identity: A Wonderful Masterpiece
	Tensor Product of a Matrix ⊗
	Postulates of Quantum Mechanics
		Postulate 1: State and Vector Space
		Postulate 2: Observables and Operators
		Postulate 3: Measurement
		Postulate 4: Collapse of the Wave Function
		Postulate 5: Unitary Transformations
	Linear Algebra and Quantum Mechanics Cheat Sheet
	Algebraic Representation of the Qubit
		Dirac’s Ket Notation
		Superposition Is a Fancy Word
		Kets Are Column Vectors
	Orient Yourself in the Bloch Sphere
	Changing the State of a Qubit with Quantum Gates
		NOT Gate (Pauli X)
		Truly Quantum: Super Positions with the Hadamard Gate
		Measurement of a Quantum State Is Trickier Than You Think
		Generalized Single Qubit Gates
		Unitary Matrices Are Good for Quantum Gates
		Other Single Qubit Gates
		Qubit Entanglement with the Controlled-NOT Gate
	Universal Quantum Computation Delivers Shortcuts over Classical Computation
	Gate Identity Cheat Sheet
	Quantum Gate vs Boolean Gate Cheat Sheet
	Exercises
Chapter 6: Qiskit, Awesome SDK for Quantum Programming in Python
	Installing Qiskit
		Setting Up in Windows
		Setting Up in Linux CentOS
			Step 1: Prepare Your System
			Step 2: Install Python 3
			Step 3: Don’t Disturb Others – Set Up a Virtual Environment
			Step 4: Install Qiskit
		Credentials Configuration
	Your First Quantum Program
		Quantum Lab: A Hidden Jewel Within the Cloud Console
			Exercise 6.1
			Exercise 6.2
			Exercise 6.3
		SDK Internals: Circuit Compilation
			Circuit Compilation
			Execution Results
			Assembly Code
			Qiskit Simulators
		Running in a Real Quantum Device
			Run via composer
			Run via Your Local Desktop
			Run via Your Favorite REST Client
				Run via the Jobs API
		Result Visualization Types
			Exercise 6.4
			Exercise 6.5
		Noise Models and Fake Providers
			Exercise 6.6
	Exercises
		Exercise 6.7
		Exercise 6.8
		Exercise 6.9
		Exercise 6.10
		Exercise 6.11
	Extended Qiskit Exercises
Chapter 7: Start Your Engines: From Quantum Random Numbers to Teleportation and Super Dense Coding
	Quantum Random Number Generation
		Random Bit Generation Using the Hadamard Gate
		Putting Randomness Results to the Test
	Super Dense Coding
		Circuit for composer
		Running in Python
		Looking at the Results
	Quantum Teleportation
		Circuit for composer
		Running in Python
		Looking at the Results
	Exercises
Chapter 8: Game Theory: With Quantum Mechanics, Odds Are Always in Your Favor
	Counterfeit Coin Puzzle
		Counterfeit Coin, the Quantum Way
		Step 1: Query the Quantum Beam Balance
		Step 2: Construct the Quantum Balance
		Step 3: Identify the False Coin
		Generalization for Any Number of False Coins
	Mermin-Peres Magic Square
		Mermin-Peres Magic Square Exercise
		Quantum Winning Strategy
		Shared Entangled State
		Unitary Transformations
		Measure in the Computational Basis
		Answers for the Mermin-Peres Magic Square Exercise
Chapter 9: Quantum Advantage with Deutsch-Jozsa, Bernstein-Vazirani, and Simon’s Algorithms
	Phase Kickback
	Kickback with Arbitrary Phases
	Deutsch-Jozsa
	Bernstein-Vazirani (BV)
	Simon’s Algorithm
		Rules for Simon Oracle Construction
		Dissecting Simon’s Oracle
	Extended Practice Exercises
Chapter 10: Advanced Algorithms: Unstructured Search and Integer Factorization with Grover and Shor
	Quantum Unstructured Search
		Phase Inversion
		Inversion About the Mean
		Practical Implementation
		Generalized Circuit
	Integer Factorization with Shor’s Algorithm
		Challenging Asymmetric Cryptography with Quantum Factorization
		Period Finding
			Fourier Sampling
			Feed the Fourier Sampling Results to Euclid Greatest Common Divisor
		Shor’s Algorithm by ProjectQ
			Factorization with ProjectQ
			Simulation Results
Chapter 11: Quantum in the Real World: Advanced Chemistry and Protein Folding
	The Significance of Eigenvalues
	Eigenvalues in a Quantum Computer
	Why Use a Quantum Computer
	Molecule Ground States
		The Lattice
		The Heisenberg Spin ½ Hamiltonian
		The VQE
		The Results
	Protein Folding
		The Protein Folding Problem
		Protein Folding Using a Quantum Computer
			Problem Initialization
			Running the VQE
			Result Interpretation and Display
			About the Peptide
	Exciting Times Lie Ahead
Appendix: Exercise Answers
	Chapter 1
	Chapter 2
	Chapter 3
	Chapter 4
	Chapter 5
	Chapter 6
	Chapter 7
	Chapter 9
Index