Contents

• Preface
• Introduction
• The Classical Computer
  • Turing Machines
  • The Church-Turing Thesis
  • Complexity Classes
  
  
• The Quantum Computer
  • Quantum Physics
  • The Classical Bit
  • State Vectors and Dirac Notation
  • Superposition and Eigenstates
  • The Qubit
  • The Quantum Memory Register
  • Probability Interpretation
  • Quantum Parallelism
  • The Power of the Quantum Computer
  
  
• Quantum Algorithms
  • Introduction to Shor's Algorithm
  • Motivation for Shor's Algorithm
  • Overview of Shor's Algorithm
  • Steps to Shor's Algorithm
  • Other Quantum Algorithms
  
  
• A Simulation of Shor's Algorithm on a Classical Computer
  • Introduction to the Code for the Simulation
  • The Complex Number Class
  • The Quantum Memory Register Class
  • The Simulation of Shor's Algorithm
  • Utility Functions for the Simulation
  
  
• Conclusion
• Bibliography
• Glossary
• Mathematics Used in this Paper
  • Binary Representation of Numbers
  • Complex Numbers
  • Vector Mathematics
  
  
• Actual Quantum Computers and Further Research
• Other Quantum Computer Simulators
• Code for my Simulation of Shor's Algorithm
  • complex.C
  • qureg.C
  • shor.C
  • util.C
  • qubit.cpp
  
  
• Sample Output
  • Sample Output for $n = 17$
  • Sample Output for $n = 15$
  • Sample Output for $n = 33$
  • Sample Output for $n = 129$