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.

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Table of Contents

Introduction:

• Quantum Computing Notation
• Postulates of Quantum Mechanics
  • 📜 1. A Quantum System
  • 🔎 2. Expected Value and Measurement Probability
  • 🌊 3. Wave function Collapse
  • 🔗 4. Composed Systems
    • Computational Basis $\mathbf{|n\rangle}$
  • 🕰️ 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

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