UsefulLinks
Computer Science
Algorithms and Data Structures
Computational Complexity Theory
1. Introduction to Computational Complexity Theory
2. Mathematical Foundations
3. Models of Computation
4. Complexity Measurement
5. Time Complexity Classes
6. Reducibility and NP-Completeness
7. Space Complexity Theory
8. Hierarchy Theorems
9. Polynomial Hierarchy
10. Randomized Complexity
11. Interactive Proof Systems
12. Circuit Complexity
13. Quantum Complexity
14. Advanced Topics
13.
Quantum Complexity
13.1.
Quantum Computation Basics
13.1.1.
Quantum Bits
13.1.1.1.
Superposition States
13.1.1.2.
Measurement Process
13.1.2.
Quantum Gates
13.1.2.1.
Unitary Operations
13.1.2.2.
Basic Gate Set
13.1.3.
Quantum Circuits
13.1.3.1.
Circuit Model
13.1.3.2.
Quantum Parallelism
13.2.
Quantum Complexity Classes
13.2.1.
Bounded-Error Quantum Polynomial Time BQP
13.2.1.1.
Definition and Properties
13.2.1.2.
Error Bounds
13.2.1.3.
Relationship to Classical Classes
13.2.2.
Exact Quantum Polynomial Time EQP
13.2.3.
Quantum Interactive Proofs QIP
13.3.
Quantum Algorithms
13.3.1.
Shor's Factoring Algorithm
13.3.1.1.
Quantum Fourier Transform
13.3.1.2.
Period Finding
13.3.1.3.
Cryptographic Implications
13.3.2.
Grover's Search Algorithm
13.3.2.1.
Unstructured Search
13.3.2.2.
Quadratic Speedup
13.3.2.3.
Optimality Results
13.3.3.
Quantum Simulation
13.4.
Quantum Complexity Theory
13.4.1.
Quantum-Classical Separations
13.4.2.
Quantum Lower Bounds
13.4.3.
Open Problems
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14. Advanced Topics