Quantum Computing From Beginner To Expert

Learning Quantum Computing through Linear Algebra

What you'll learn

Introduction of Quantum Computing

Bloch Sphere

Basic Logic Gates for Single Qubit

Rotation Logic Gates for Single Qubit

Multi-Qubit Logic Gates

Quantum Measurement

Quantum Circuits

Algorithms： Amplitude Amplification

Algorithms： Quantum Fourier Transform

Algorithms： Quantum Phase Estimation

Algorithms： Quantum Arithmetic Operations

Algorithms： HHL Algorithm

Algorithms： Deutsch-Josza Algorithm

Algorithms： Grover Algorithm

Requirements

High school level mathematics: Complex numbers, linear algebra, probability, statistics, & boolean logic

Description

This comprehensive course is suitable for a wide range of learners, from those who are just beginning to explore quantum computing to experts in the field. Our aim is to cover every aspect of quantum computing, starting from the basics and progressing to complex application scenarios. Unlike other courses, we place a strong emphasis on learning quantum computing through linear algebra and provide detailed matrices and vector calculations for key concepts, allowing you to develop a solid understanding of the subject matter.The course is divided into two main parts, each of which is designed to provide learners with a deep understanding of quantum computing:Basic part, which includes:An overview of quantum computing, quantum bits, single quantum bit logical gates, multi-quantum bit logical gates, quantum measurement, quantum circuits, and more.Algorithm part, which includes:The Hadamard Test, SWAP Test, amplitude amplification, quantum Fourier transform, quantum phase estimation, quantum arithmetic, the HHL algorithm, Deutsch-Josza algorithm, Grover algorithm, and more.But that's not all - we're continually updating and improving the course to include even more valuable information, such as:Programming part, which includes:Examples of basic logic gates based on Qiskit, as well as learning examples of algorithms.Machine learning part, which includes:Algorithms and implementations of quantum machine learning and quantum artificial intelligence.Application part, which includes:The application of quantum computing technology in finance and other fields, allowing you to gain a broader understanding of how quantum computing is transforming industries and changing the face of technology.

Overview

Section 1: Fundamentals: Introduction of Quantum Computing

Lecture 1 Introduction

Lecture 2 A Brief History of Quantum Computing

Lecture 3 Main Application Areas

Section 2: Fundamentals: Complex Numbers and Linear Algebra

Lecture 4 Complex Numbers

Lecture 5 Relationship between Complex Numbers and Vectors

Lecture 6 Hilbert Space and Euclidean Space Conversion

Lecture 7 Comparison of Matrix Types

Lecture 8 Symmetric Matrix and Hermitian Matrix

Lecture 9 Orthogonal Matrix and Unitary Matrix

Section 3: Fundamentals: Quantum Bits (Qubits)

Lecture 10 Dirac notation

Lecture 11 Single Qubit

Lecture 12 Multi-Qubit System

Section 4: Fundamentals: Bloch Sphere

Lecture 13 Introduction

Lecture 14 Global Phase

Lecture 15 Dimension Reduction

Lecture 16 Half Angles

Lecture 17 Bloch Sphere

Section 5: Fundamentals: Basic Logic Gates for Single Qubit

Lecture 18 Unitary Transformation

Lecture 19 Hermitian Conjugate Operator - Common Formulas

Lecture 20 How to calculate the unitary transformation matrix for a single qubit

Lecture 21 Hadamard Gate

Lecture 22 Pauli Operator

Lecture 23 Pauli-X Gate

Lecture 24 Pauli-Y Gate

Lecture 25 Pauli-Z Gate

Section 6: Fundamentals: Rotation Logic Gates for Single Qubit

Lecture 26 Exponential Function of Matrices

Lecture 27 Generator - Pauli Matrices

Lecture 28 Density Operator (Matrix)

Lecture 29 3D Rotations in Four-Dimensional Space

Lecture 30 RX(θ) Gate

Lecture 31 RY(θ) Gate

Lecture 32 RZ(θ) Gate

Section 7: Fundamentals: Multi-Qubit Logic Gates

Lecture 33 Tensor Product

Lecture 34 How to calculate the unitary matrix for a two-qubit system?

Lecture 35 CNOT Gate

Lecture 36 SWAP Gate

Lecture 37 How to calculate the unitary matrix for a three-qubit system?

Lecture 38 Toffoli (CCNOT) Gate

Lecture 39 Fredkin (CSWAP) Gate

Section 8: Fundamentals: Quantum Measurement

Lecture 40 Measurement and Collapse

Lecture 41 The Hermitian adjoint operator and common formulas

Lecture 42 Normal Matrix

Lecture 43 Completeness Equation

Lecture 44 Projection Operator

Lecture 45 Projective Measurements

Lecture 46 Measurement of a Single Qubit

Lecture 47 Measurement of a Two-qubit System

Section 9: Fundamentals: Quantum Circuits

Lecture 48 Introduction to Quantum Circuits

Lecture 49 X Gate, Y Gate, Z Gate, H Gate

Lecture 50 RX(θ) Gate, RY(θ) Gate, RZ(θ) Gate

Lecture 51 CNOT Gate, SWAP Gate, Toffoli Gate

Section 10: Algorithms: Hadamard Test、SWAP Test

Lecture 52 Quantum entanglement

Lecture 53 Hadamard Test - Real part

Lecture 54 Hadamard Test – Imaginary part

Lecture 55 SWAP Test

Section 11: Algorithms: Amplitude Amplification

Lecture 56 2D Geometric Transformations

Lecture 57 Transformation in Arbitrary Dimensions

Lecture 58 Introduction to Amplitude Amplification

Lecture 59 Amplitude Amplification Operator

Section 12: Algorithms: Quantum Fourier Transform

Lecture 60 Fourier series & Fourier transform

Lecture 61 Fourier Transform, DFT, IDFT

Lecture 62 Quantum Fourier Transform

Section 13: Algorithms: Quantum Phase Estimation

Lecture 63 Introduction

Lecture 64 Quantum Circuit

Lecture 65 Quantum Phase Estimation - Steps

Section 14: Algorithms: Quantum Arithmetic Operations

Lecture 66 Logic Gates

Lecture 67 One-bit Adder

Lecture 68 Multi-bit Adder

Lecture 69 Quantum Subtractor,Multiplier,Divider

Section 15: Algorithms: HHL Algorithm

Lecture 70 Overview of HHL Quantum Algorithm

Lecture 71 HHL Algorithm Quantum Circuit

Section 16: Algorithms: Deutsch-Josza Algorithm

Lecture 72 Deutsch–Jozsa Problem

Lecture 73 Oracle - Quantum Circuit

Lecture 74 Oracle - Simplification of Quantum Circuits

Lecture 75 Deutsch Algorithm

Lecture 76 Deutsch-Jozsa Algorithm

Section 17: Algorithms: Grover Algorithm

Lecture 77 Reflection and Mirror Transformation

Lecture 78 Grover‘s Search Algorithm

Lecture 79 Grover Algorithm - Two Qubits

Lecture 80 Grover Algorithm - N Qubits

Students who want to learn about Quantum Computing,Quantum Computing enthusiasts