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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.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: The Problem Shor Solves5
- Chapter 2: Classical Computation, Complexity, and Reversibility6
- Chapter 3: Qubits from Linear Algebra7
- Chapter 4: Quantum Gates and Circuits8
- Chapter 5: Superposition, Interference, and Entanglement9
- Chapter 6: Number Theory for Factoring10
- Chapter 7: From Factoring to Order Finding11
- Chapter 8: Periodic Functions and Hidden Structure12
- Chapter 9: The Quantum Fourier Transform13
- Chapter 10: Building the QFT Circuit14
- Chapter 11: Quantum Phase Estimation15
- Chapter 12: Modular Exponentiation as a Quantum Operation16
- Chapter 13: The Full Shor Factoring Algorithm17
- Chapter 14: Why the Measurement Reveals the Period18
- Chapter 15: Continued Fractions and Classical Postprocessing19
- Chapter 16: Worked Examples by Hand20
- Chapter 17: Correctness, Runtime, and Success Probability21
- Chapter 18: Shor's Algorithm for Discrete Logarithms22
- Chapter 19: The Hidden Subgroup Perspective23
- Chapter 20: Applying the Principles to New Problems24
- Chapter 21: Limits, Noise, and Real Hardware25
- Chapter 22: Cryptographic Consequences26
- Chapter 23: Implementing and Simulating Shor's Algorithm27
- Chapter 24: Mastery Map and Further Directions28
- Conclusion29