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Table of contents
Classical and Quantum Query Complexity
From decision-tree foundations to modern adversary methods, span programs, and research frontiers in quantum algorithms
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 Query Model as a Theory of Information Access5
- Chapter 2: Mathematical Foundations for Query Complexity6
- Chapter 3: Deterministic Decision Trees7
- Chapter 4: Randomized Query Algorithms8
- Chapter 5: Classical Lower-Bound Methods9
- Chapter 6: Boolean Function Measures and Structural Complexity10
- Chapter 7: The Polynomial Method in Classical Query Complexity11
- Chapter 8: Quantum Computation Preliminaries12
- Chapter 9: The Quantum Query Model13
- Chapter 10: First Quantum Query Algorithms14
- Chapter 11: Grover Search and Amplitude Amplification15
- Chapter 12: Quantum Lower Bounds I: The Polynomial Method16
- Chapter 13: Approximate Degree in Depth17
- Chapter 14: Quantum Lower Bounds II: Hybrid and Adversary Methods18
- Chapter 15: The General Adversary Bound19
- Chapter 16: Span Programs and Algorithm Design20
- Chapter 17: Composition, Direct Sums, and Product Phenomena21
- Chapter 18: Total Functions, Partial Functions, and Separations22
- Chapter 19: Query Complexity of Graph, Property, and Symmetry Problems23
- Chapter 20: Quantum Walks and Query Algorithms24
- Chapter 21: Learning Graphs, Certificate Structures, and Advanced Algorithmic Frameworks25
- Chapter 22: Beyond Boolean Functions: Relations, State Conversion, and Nonstandard Oracles26
- Chapter 23: Connections to Communication Complexity, Learning Theory, and Cryptography27
- Chapter 24: Research Frontiers in Classical and Quantum Query Complexity28
- Conclusion29