Quantum Computing

  1. Quantum Software and Programming
    1. Quantum Programming Models
      1. Circuit-Based Model
        1. Gate-Level Programming
          1. Circuit Depth and Width
            1. Quantum Assembly Languages
            2. Adiabatic and Annealing Models
              1. Quantum Annealing Principles
                1. Problem Mapping
                  1. Ising Model Formulation
                  2. Measurement-Based Quantum Computation
                    1. Cluster States
                      1. One-Way Quantum Computing
                        1. Graph States
                        2. Topological Quantum Computing Model
                        3. Quantum Programming Languages
                          1. High-Level Quantum Languages
                            1. Q#
                              1. Qiskit
                                1. Cirq
                                  1. Silq
                                  2. Quantum Assembly Languages
                                    1. OpenQASM
                                      1. Quil
                                      2. Classical-Quantum Hybrid Languages
                                      3. Quantum Software Development Kits (SDKs)
                                        1. IBM Qiskit
                                          1. Circuit Construction
                                            1. Quantum Algorithms Library
                                              1. Hardware Access
                                              2. Google Cirq
                                                1. NISQ-Era Focus
                                                  1. Hardware Integration
                                                  2. Xanadu PennyLane
                                                    1. Quantum Machine Learning
                                                      1. Differentiable Programming
                                                      2. Microsoft Quantum Development Kit
                                                        1. Other Notable SDKs
                                                          1. Rigetti Forest
                                                            1. IonQ SDK
                                                            2. Programming at the Pulse Level
                                                              1. Pulse Schedules
                                                                1. Hardware Calibration
                                                                  1. Low-Level Control
                                                                2. Quantum Compilers and Transpilers
                                                                  1. Gate Synthesis
                                                                    1. Decomposition into Native Gates
                                                                      1. Approximation Algorithms
                                                                      2. Circuit Optimization
                                                                        1. Reducing Gate Count
                                                                          1. Minimizing Circuit Depth
                                                                            1. Commutation Relations
                                                                            2. Mapping to Hardware Topologies
                                                                              1. Qubit Routing
                                                                                1. Connectivity Constraints
                                                                                  1. SWAP Insertion
                                                                                  2. Error Mitigation Techniques
                                                                                    1. Zero-Noise Extrapolation
                                                                                      1. Readout Error Mitigation
                                                                                        1. Symmetry Verification
                                                                                      2. Accessing Quantum Hardware
                                                                                        1. Cloud-Based Quantum Computing Platforms
                                                                                          1. IBM Quantum Network
                                                                                            1. Google Quantum AI
                                                                                              1. Amazon Braket
                                                                                                1. Microsoft Azure Quantum
                                                                                                2. Quantum Simulators
                                                                                                  1. Classical Simulation of Quantum Circuits
                                                                                                    1. Limitations and Use Cases
                                                                                                      1. Noise Simulation
                                                                                                      2. Hybrid Computing Architectures

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                                                                                                    9. Applications and Impact

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                                                                                                    11. Advanced Topics and Future Directions