Module 02 of 10

Math Foundations

Lessons

About This Module

Quantum computing looks intimidating mostly because of its notation, not its ideas. Almost everything you'll meet later, from qubits to gates to algorithms, is built from a small amount of linear algebra. This module gives you just enough of that math to read quantum states and operations without getting lost.

It starts with vectors and builds a geometric feel for what they are, then moves to linear transformations and matrices, which are how every quantum gate is described. A lesson on abstract vector spaces shows why the same math works for things that aren't arrows. It closes with Dirac notation, the bra-ket shorthand used to write quantum states and measurements throughout the field.

Watch the lessons in order, then continue on to Qubits & Superposition.

Lessons

4 videos
01

Vectors | Essence of Linear Algebra, Chapter 1

3Blue1Brown's visual introduction to vectors from three angles (arrows, lists of numbers, and abstract objects), the foundation for describing quantum states.

02

Linear Transformations and Matrices | Essence of Linear Algebra, Chapter 3

Why matrices are best understood as transformations of space, which is exactly how quantum gates act on qubits.

03

Abstract Vector Spaces | Essence of Linear Algebra, Chapter 16

Why the rules of linear algebra apply to far more than arrows and number lists, the idea behind the state spaces used in quantum mechanics.

04

Single Systems | Understanding Quantum Information & Computation, Lesson 01

Qiskit's lesson on Dirac notation: kets, bras, and inner products, and how quantum states are written as vectors.