Quantum Computing: From Basics to Advanced Algorithms

This introductory course develops the mathematical foundations of quantum computing before covering qubits, quantum gates, quantum circuits, entanglement, and algorithms such as Deutsch-Jozsa, Bernstein-Vazirani, and Shor’s algorithm.

Syllabus

⌨️ Introduction
⌨️ 0.1 Introduction to Complex Numbers
⌨️ 0.2 Complex Numbers on the Number Plane
⌨️ 0.3 Introduction to Matrices
⌨️ 0.4 Matrix Multiplication to Transform a Vector
⌨️ 0.5 Unitary and Hermitian Matrices
⌨️ 0.6 Eigenvectors and Eigenvalues
⌨️ 1.1 Introduction to Qubit and Superposition
⌨️ 1.2 Introduction to Dirac Notation
⌨️ 1.3 Representing a Qubit on the Bloch Sphere
⌨️ 1.4 Manipulating a Qubit with Single Qubit Gates
⌨️ 1.5 Introduction to Phase
⌨️ 1.6 The Hadamard Gate and +, -, i, -i States
⌨️ 1.7 The Phase Gates S and T Gates
⌨️ 2.1 Representing Multiple Qubits Mathematically
⌨️ 2.2 Quantum Circuits
⌨️ 2.3 Multi-Qubit Gates
⌨️ 2.4 Measuring Singular Qubits
⌨️ 2.5 Quantum Entanglement and the Bell States
⌨️ 2.6 Phase Kickback
⌨️ 3.1 Superdense Coding
⌨️ 3.2.A Classical Operations Prerequisites
⌨️ 3.2.B Functions on Quantum Computers
⌨️ 3.3 Deutsch's Algorithm
⌨️ 3.4 Deutch-Jozsa Algorithm
⌨️ 3.5 Berstein-Vazarani Algorithm
⌨️ 3.6 Quantum Fourier Transform QFT
⌨️ 3.7 Quantum Phase Estimation
⌨️ 3.8 Shor's Algorithm