Introduction to Classical and Quantum Computing

Classical Information and Computation
	Bits
		Coins
		Dice
		Encoding Information
		Physical Bits
		Binary
		ASCII
	Logic Gates
		Single-Bit Gates
		Two-Bit Gates
		Logic Gates as Physical Circuits
		Multiple Gates
		Universal Gates
	Adders and Verilog
		Adding Binary Numbers by Hand
		Half Adder
		Full Adder
		Ripple-Carry Adder
		Ripple-Carry with Full Adders
		Circuit Complexity
	Circuit Simplification and Boolean Algebra
		Order of Operations
		Association, Commutivity, and Distribution
		Identities Involving Zero and One
		Single-Variable Identities
		Two-Variable Identities and De Morgan's Laws
		Circuit Simplification
	Reversible Logic Gates
		Reversible Gates
		Irreversible Gates
		Toffoli Gate: A Reversible AND Gate
		Making Irreversible Gates Reversible
	Error Correction
		Errors in Physical Devices
		Error Detection
		Error Correction
	Computational Complexity
		Asymptotic Notation
		Complexity Classes
	Turing Machines
		Components
		Incrementing Binary Numbers
		Church-Turing Thesis
	Summary
One Quantum Bit
	Qubit Touchdown: A Quantum Computing Board Game
	Superposition
		Zero or One
		Superposition
		Review of Complex Numbers
	Measurement
		Measurement in the Z-Basis
		Normalization
		Measurement in Other Bases
		Consecutive Measurements
	Bloch Sphere Mapping
		Global and Relative Phases
		Spherical Coordinates
		Cartesian Coordinates
	Physical Qubits
	Quantum Gates
		Linear Maps
		Classical Reversible Gates
		Common One-Qubit Quantum Gates
		General One-Qubit Gates
	Quantum Circuits
		Circuit Diagrams
		Quirk
	Summary
Linear Algebra
	Quantum States
		Column Vectors
		Row Vectors
	Inner Products
		Inner Products Are Scalars
		Orthonormality
		Projection, Measurement, and Change of Basis
	Quantum Gates
		Gates as Matrices
		Common One-Qubit Gates as Matrices
		Sequential Quantum Gates
		Circuit Identities
		Unitarity
		Reversibility
	Outer Products
		Outer Products Are Matrices
		Completeness Relation
	Summary
Multiple Quantum Bits
	Entanglion: A Quantum Computing Board Game
		Mechanics
		Connection to Quantum Computing
	States and Measurement
		Tensor Product
		Kronecker Product
		Measuring Individual Qubits
		Sequential Single-Qubit Measurements
	Entanglement
		Product States
		Entangled States
	Quantum Gates
		One-Qubit Quantum Gates
		Two-Qubit Quantum Gates
		Toffoli Gate
		No-Cloning Theorem
	Quantum Adders
		Classical Adder
		Making the Classical Adder a Quantum Gate
		Quantum Setup
		Quantum Sum
		Quantum Carry
		Quantum Ripple-Carry Adder
		Circuit Complexity
		Adding in Superposition
	Universal Quantum Gates
		Definition
		Components of a Universal Gate Set
		Examples of Universal Gate Sets
		Solovay-Kitaev Theorem
		Quantum Computing without Complex Numbers
	Quantum Error Correction
		Decoherence
		Bit-Flip Code
		Phase-Flip Code
		Shor Code
	Summary
Quantum Programming
	IBM Quantum Experience
		Services
		Circuit Composer
		Quantum Processor
		Simulator
	Quantum Assembly Language
		OpenQASM
		Quantum Experience Standard Header
		OpenQASM in IBM Quantum Experience
		Quantum Adder
	Qiskit
		Circuit Composer
		Quantum Lab
		Simulator
		Quantum Processor
	Other Quantum Programming Languages
	Summary
Entanglement and Quantum Protocols
	Measurements
		Product States
		Maximally Entangled States
		Partially Entangled States
	Bell Inequalities
		EPR Paradox and Local Hidden Variables
		Bell Inequalities and the CHSH Inequality
		Quantum Processor Experiment
		Other Experiments
		No-Signaling Principle
		Other Theories
	Monogamy of Entanglement
		Classical Correlations
		Quantum Entanglement
	Superdense Coding
		The Problem
		Classical Solution
		Quantum Solution
	Quantum Teleportation
		The Problem
		Classical Solution
		Quantum Solution
	Quantum Key Distribution
		Encryption
		Classical Solution: Public Key Cryptography
		Quantum Solution: BB84
	Summary
Quantum Algorithms
	Circuit vs Query Complexity
		Circuit Complexity
		Query Complexity
		Quantum Oracles
		Phase Oracle
	Parity
		The Problem
		Classical Solution
		Quantum Solution: Deutsch's Algorithm
		Generalization to Additional Bits
	Constant vs Balanced Functions
		The Problem
		Classical Solution
		Quantum Solution: Deutsch-Jozsa Algorithm
	Secret Dot Product String
		The Problem
		Classical Solution
		Quantum Solution: Bernstein-Vazirani Algorithm
		Recursive Problem
	Secret XOR Mask
		The Problem
		Classical Solution
		Quantum Solution: Simon's Algorithm
		Summary
	Brute-Force Searching
		The Problem
		Classical Solution
		Quantum Solution: Grover's Algorithm
		Reflection About Uniform State
		Optimality
	Discrete Fourier Transform
		Application: Analyzing Music
		Classical Solution: Fast Fourier Transform
		Quantum Solution: Quantum Fourier Transform
		Inverse Quantum Fourier Transform
	Phase / Eigenvalue Estimation
		The Problem
		Classical Solution
		Quantum Solution
		Multiple Eigenstates
	Period of Modular Exponentiation
		The Problem
		Classical Solution
		Quantum Solution
	Factoring
		The Problem
		Classical Solution
		Quantum Solution: Shor's Algorithm
	Summary
Next Steps
	Careers in Quantum Computing
	Technical Next Steps
	Questions
	Parting Words
Answers to Exercises
Index