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