Quantum Computing
After strengthening my mathematical skills and establishing a solid foundation in linear algebra, I delved into quantum computing through Nielsen and Chuang’s Quantum Computation and Quantum Information. I approached each topic in the book with a keen focus on understanding its mathematical constructs and nuances. Frequently, my curiosity led me to explore beyond the book, engaging with additional materials to broaden my perspective and deepen my understanding. The Quantum Computing Stack Exchange has been an invaluable resource in navigating these challenges independently, often sparking extended discussions that enriched my understanding. Mathematics Stack Exchange has similarly played a pivotal role in helping me grasp the mathematical framework of quantum computing concepts.
These notes are an attempt to organize and share what I’ve learned over the years. They encompass not only the material from Nielsen and Chuang’s book but also the extended explorations and insights I’ve gained through tackling complex questions and problems. Having enrolled in CS5001 Introduction to Quantum Computing at Missouri S&T, my notes extend well beyond the scope of a typical 5000-level graduate course.
Book 1: Introduction to Quantum Computing
- Postulates of Quantum Mechanics (p.3)
- Distinguishing Quantum States (p.46)
- Projective Measurement (p.56)
- POVM Measurement (p.73)
- General Measurement=Projective+Unitary
- Superdense Coding (p.106)
- Tensor Product (p.121)
- Multipartite System (p.165)
- Schmidt Decomposition (p.182)
- Quantum Measurement Revisited (p.191)
Book 2: Density Matrix Formalism
Book 3: Quantum Computation
Book 4: More Quantum Computation
Book 5: Universal Quantum Gates
Book 6: Simulating Quantum Systems
Book 7: Quantum Fourier Transform
- Quantum Parallelism (p.5)
- Deutsch's Algorithm (p.10)
- Deutsch-Jozsa Algorithm (p.16)
- Probabilistic Classical Algorithm
- Discrete Fourier Transform (p.35)
- Quantum Fourier Transform (p.50)
- QFT Circuit (p.58)
- Inverse QFT (p.75)
- Approximating QFT (p.77)
- Phase Estimation (p.79)
- Performance of Phase Estimation (p.97)
Book 8: More Quantum Algorithms
Book 9: Hidden Subgroup Problem
Book 10: Quantum Search
Book 11:
Book 12: Quantum Operations
Book 13: Quantum Noice
Book 14: Quantum Tomography
Chapter 9: Distance Measures
Chapter 10: Quantum Error Correction
Chapter 11 (Part 1): Entropy and Information
Chapter 11 (Part 2): Entropy and Information
- Von Neumann Entropy
- Complex Logarithm
- Quantum Relative Entropy
- Klein's Inequality
- Contunuity of Entropy
- Properties Von Neumann Entropy
- $AB$ is pure state$\implies S(A)=S(B)$
- Joint Entropy Theorem
- Entropy of Tensor Product
- Entanglement and Negative Conditional Entropy
- Measurement and Entropy
- Projective Measurement Increases Entropy
- Generalized Measurement can Decrease Entropy
- Subadditivity
- Triangle Inequality
- Concavity of Entropy
- Entropy of a Mixture of States
- Strong Subadditivity