Introduction to Classical and Quantum Computing
# Introduction to Classical and Quantum Computing
Metadata
- CiteKey:: wongIntroductionClassicalQuantum
- Type:: book
- Author:: Thomas Wong
- Year:: 2022
- Tags:: #Source/Zotero, #Source/Book
- Format:: PDF
- Rating:: 10
Abstract
I wrote a FREE introductory quantum computing textbook! The only prerequisite is trigonometry. It is not a conceptual overview, however. Rather, it teaches the math (including basic linear algebra) along the way.The textbook is based on an introductory quantum computing course that I’ve been teaching at Creighton University since 2018. From the beginning, I wrote all my lecture notes and homework problems in a textbook format using LaTeX, and now they’re available to everyone.
Files and Links
Tags and Collections
- Keywords:: Book; Quantum Computing; 📥
Table of contents
- Chapter 1 - 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
- 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
- Chapter 2 - 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
- Bloch Sphere
- Physical Qubits
- Quantum Gates
- Linear Maps
- Classical Reversible Gates
- Common One-Qubit Quantum Gates
- General One-Qubit Gates
- Quantum Circuits
- Summary
- Chapter 3 - 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
- Chapter 4 - 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
- Chapter 5 - 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
- Chapter 6 - 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
- Chapter 7 - 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
- 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
- Chapter 8 - Next Steps
- Careers in Quantum Computing
- Technical Next Steps
- Questions
- Parting Words
Answers to Exercises
Index