Computational Complexity Theory

  1. Quantum Complexity
    1. Quantum Computation Basics
      1. Quantum Bits
        1. Superposition States
          1. Measurement Process
          2. Quantum Gates
            1. Unitary Operations
              1. Basic Gate Set
              2. Quantum Circuits
                1. Circuit Model
                  1. Quantum Parallelism
                2. Quantum Complexity Classes
                  1. Bounded-Error Quantum Polynomial Time BQP
                    1. Definition and Properties
                      1. Error Bounds
                        1. Relationship to Classical Classes
                        2. Exact Quantum Polynomial Time EQP
                          1. Quantum Interactive Proofs QIP
                          2. Quantum Algorithms
                            1. Shor's Factoring Algorithm
                              1. Quantum Fourier Transform
                                1. Period Finding
                                  1. Cryptographic Implications
                                  2. Grover's Search Algorithm
                                    1. Quadratic Speedup
                                      1. Optimality Results
                                      2. Quantum Simulation
                                      3. Quantum Complexity Theory
                                        1. Quantum-Classical Separations
                                          1. Quantum Lower Bounds
                                            1. Open Problems

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                                          14. Advanced Topics