Table of contents

Shor's Algorithm from First Principles

A clear undergraduate path from quantum mechanics and number theory to period finding, factoring, and transferable quantum algorithm design

Read each section in order. Every title can be opened as a TheoryTrace document.

• Cover
• Copyright
• How to read this book
• Introduction
• Chapter 1: The Problem Shor Solves
• Chapter 2: Classical Computation, Complexity, and Reversibility
• Chapter 3: Qubits from Linear Algebra
• Chapter 4: Quantum Gates and Circuits
• Chapter 5: Superposition, Interference, and Entanglement
• Chapter 6: Number Theory for Factoring
• Chapter 7: From Factoring to Order Finding
• Chapter 8: Periodic Functions and Hidden Structure
• Chapter 9: The Quantum Fourier Transform
• Chapter 10: Building the QFT Circuit
• Chapter 11: Quantum Phase Estimation
• Chapter 12: Modular Exponentiation as a Quantum Operation
• Chapter 13: The Full Shor Factoring Algorithm
• Chapter 14: Why the Measurement Reveals the Period
• Chapter 15: Continued Fractions and Classical Postprocessing
• Chapter 16: Worked Examples by Hand
• Chapter 17: Correctness, Runtime, and Success Probability
• Chapter 18: Shor's Algorithm for Discrete Logarithms
• Chapter 19: The Hidden Subgroup Perspective
• Chapter 20: Applying the Principles to New Problems
• Chapter 21: Limits, Noise, and Real Hardware
• Chapter 22: Cryptographic Consequences
• Chapter 23: Implementing and Simulating Shor's Algorithm
• Chapter 24: Mastery Map and Further Directions
• Conclusion