Table of contents

Quantum Computing for Mathematicians

A rigorous path from Hilbert spaces and unitary dynamics to algorithms, complexity, and quantum error correction

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 Mathematical Shape of Quantum Computation
• Chapter 2: Finite-Dimensional Hilbert Spaces and Tensor Products
• Chapter 3: Qubits, States, and the Bloch Sphere
• Chapter 4: Postulates as Operational Mathematics
• Chapter 5: Density Operators, Partial Trace, and Open Systems
• Chapter 6: Entanglement and Nonclassical Correlations
• Chapter 7: Reversible Classical Computation and Quantum Circuits
• Chapter 8: Universal Quantum Computation
• Chapter 9: Quantum Fourier Transform and Phase Estimation
• Chapter 10: Shor’s Algorithm and the Hidden Subgroup Perspective
• Chapter 11: Amplitude Amplification and Grover Search
• Chapter 12: Quantum Algorithms Beyond the Classics
• Chapter 13: Quantum Complexity Theory
• Chapter 14: Quantum Information Measures
• Chapter 15: Quantum Error Correction
• Chapter 16: Stabilizer Formalism and Clifford Computation
• Chapter 17: Fault Tolerance and Threshold Theorems
• Chapter 18: Hamiltonian Models and Adiabatic Computation
• Chapter 19: Measurement-Based Quantum Computation
• Chapter 20: Mathematical Frontiers and Research Literacy
• Conclusion