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Mathematical Foundations of Quantum Algorithms

This project explores quantum algorithms through the lens of Qiskit, providing a foundation based on the postulates of quantum mechanics. It covers essential quantum gates, massive quantum parallelism, entanglement and Bell states, and fundamental quantum algorithms such as quantum teleportation.


Table of Contents

Introduction:

  • Quantum Computing Notation
  • Postulates of Quantum Mechanics
    • πŸ“œ 1. A Quantum System
    • πŸ”Ž 2. Expected Value and Measurement Probability
    • 🌊 3. Wave function Collapse
    • πŸ”— 4. Composed Systems
      • Computational Basis $\mathbf{|n\rangle}$
    • πŸ•°οΈ 5. Time Evolution
      • Pauli Gates
      • Hadamard Gate
      • Phase Shift Gate

Key Principles in Quantum Computing:

  • Massive Quantum Parallelism
  • CNOT Gate
  • SWAP Gate
  • $|\pm\rangle$ Bases
  • Entanglement and Bell States

Quantum Algorithm:

  • Quantum teleportation

The project focuses on mathematical understanding while demonstrating simple implementations in Qiskit. πŸš€