QUANTUM-COMPUTING-TOPICS-MWALALEARN

Objectives: Topics to be covered

Quantum Computing Complete Topics

Quantum Computing Complete Topics

1. Foundations of Mathematics and Physics

  • Linear Algebra
    • Vectors & inner products
    • Complex numbers
    • Tensor products
    • Hermitian, unitary, and projection operators
  • Probability & Statistics
    • Random variables and distributions
    • Expectation values
    • Markov chains
  • Quantum Mechanics
    • Postulates of quantum mechanics
    • Superposition principle
    • Measurement postulate
    • Uncertainty principle
    • Entanglement & Bell’s inequalities

2. Quantum Information Science

  • Qubits and Hilbert Space
    • Representation of qubits
    • Bloch sphere
    • Multi-qubit systems
  • Quantum Gates & Circuits
    • Single qubit gates (X, Y, Z, H, S, T, Rφ)
    • Multi-qubit gates (CNOT, Toffoli, Fredkin, Swap)
    • Universal gate sets
  • Quantum Measurements
    • Projective measurements
    • POVMs (Positive Operator Valued Measures)
  • Quantum Entanglement
    • EPR pairs
    • Bell states
    • GHZ states

3. Quantum Algorithms

  • Basic Algorithms
    • Deutsch-Jozsa
    • Bernstein-Vazirani
    • Simon’s algorithm
  • Search & Optimization
    • Grover’s algorithm
    • Amplitude amplification
    • Quantum annealing
  • Number Theory & Cryptography
    • Shor’s algorithm (factoring)
    • Quantum Fourier Transform (QFT)
    • Order-finding
  • Linear Systems & Simulation
    • HHL algorithm
    • Quantum phase estimation
    • Variational quantum eigensolver (VQE)
    • Quantum approximate optimization algorithm (QAOA)

4. Quantum Error Correction & Noise

  • Quantum Decoherence
    • Noise models (bit-flip, phase-flip, depolarizing)
  • Quantum Error Correcting Codes
    • Shor code
    • Steane code
    • Surface codes
    • Stabilizer formalism
  • Fault-Tolerant Quantum Computing
    • Threshold theorem
    • Logical vs. physical qubits

5. Quantum Complexity Theory

  • Computational Complexity Classes
    • P, NP, BPP
    • BQP (Bounded-error Quantum Polynomial-time)
    • QMA (Quantum Merlin-Arthur)
  • Quantum Supremacy
    • Definition and meaning
    • Demonstrations by Google (Sycamore), IBM, etc.

6. Quantum Cryptography & Communication

  • Quantum Key Distribution (QKD)
    • BB84 protocol
    • E91 protocol
  • Post-Quantum Cryptography
    • Lattice-based cryptography
    • Code-based & multivariate cryptography
  • Quantum Teleportation
    • Protocol
    • Applications in quantum networks
  • Quantum Networks & Internet
    • Quantum repeaters
    • Entanglement swapping
    • Future of quantum internet

7. Quantum Hardware & Technologies

  • Types of Qubits
    • Superconducting qubits
    • Trapped ions
    • Photonic qubits
    • Topological qubits
    • Spin qubits
  • Quantum Control & Measurement
    • Pulse shaping
    • Readout techniques
  • Scalability Challenges
    • Qubit coherence times
    • Gate fidelities
    • Error rates

8. Quantum Software & Frameworks

  • Programming Languages & SDKs
    • Qiskit (IBM)
    • Cirq (Google)
    • Braket (Amazon)
    • Ocean (D-Wave)
  • Quantum Cloud Services
    • IBM Quantum Experience
    • Microsoft Azure Quantum
    • Amazon Braket
    • Xanadu (PennyLane)
  • Hybrid Quantum-Classical Computing
    • Variational algorithms
    • Machine learning with quantum processors

9. Quantum Machine Learning (QML)

  • Foundations
    • Quantum data encoding
    • Quantum feature spaces
  • Algorithms
    • Quantum kernel methods
    • Quantum neural networks
    • Quantum generative models
  • Applications
    • Chemistry & drug discovery
    • Finance & portfolio optimization
    • AI acceleration

10. Frontiers of Research

  • Topological Quantum Computing
    • Anyons
    • Majorana fermions
  • Quantum Gravity & Computing
    • Holographic principle
    • AdS/CFT connections
  • Quantum Biology
    • Quantum effects in photosynthesis
    • Quantum tunneling in enzymes
    • Quantum consciousness debates

11. Ethics, Policy & Economics

  • Cybersecurity threats & opportunities
  • Regulation & international competition
  • Quantum economy & startups
  • Societal impact & ethics

Reference Book: N/A

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