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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.
- Cover1
- Copyright2
- How to read this book3
- Introduction4
- Chapter 1: The Mathematical Shape of Quantum Computation5
- Chapter 2: Finite-Dimensional Hilbert Spaces and Tensor Products6
- Chapter 3: Qubits, States, and the Bloch Sphere7
- Chapter 4: Postulates as Operational Mathematics8
- Chapter 5: Density Operators, Partial Trace, and Open Systems9
- Chapter 6: Entanglement and Nonclassical Correlations10
- Chapter 7: Reversible Classical Computation and Quantum Circuits11
- Chapter 8: Universal Quantum Computation12
- Chapter 9: Quantum Fourier Transform and Phase Estimation13
- Chapter 10: Shor’s Algorithm and the Hidden Subgroup Perspective14
- Chapter 11: Amplitude Amplification and Grover Search15
- Chapter 12: Quantum Algorithms Beyond the Classics16
- Chapter 13: Quantum Complexity Theory17
- Chapter 14: Quantum Information Measures18
- Chapter 15: Quantum Error Correction19
- Chapter 16: Stabilizer Formalism and Clifford Computation20
- Chapter 17: Fault Tolerance and Threshold Theorems21
- Chapter 18: Hamiltonian Models and Adiabatic Computation22
- Chapter 19: Measurement-Based Quantum Computation23
- Chapter 20: Mathematical Frontiers and Research Literacy24
- Conclusion25