Mathematical Basics
Overview
Overview
In this set of lessons, students are introduced to the basic mathematical tools they need to carry out (most of) the other lessons in this project. The lessons on probabilities and matrices are compulsory. The optional lessons introduce students to vector calculation, complex numbers and the Bloch sphere. All lessons come with exercises.
Keywords: Probability, matrices, vectors, complex numbers, Bloch sphere
Age group: 14-18 years
Required knowledge/skills: Basic algebra
Time frame: 30-45 minutes per topic
Author: Natalija Budinski (RS)
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Probability – From classical to quantum
Quick introduction to complex numbers
Vectors
Matrices and how they can be used in quantum computing
Using the Bloch sphere to represent a qubit
Probability – From classical to quantum
In this lesson, students will explore the concept of probability through both classical and quantum perspectives.
Quick Introduction to Complex Numbers
In this lesson, students will be introduced to complex numbers and to how they are used in both mathematics and quantum computing.
Vectors
Students explore the core ideas behind vectors, from geometric and coordinate representations to essential operations. The unit concludes by linking these principles to quantum computing, where vectors are used to represent qubit states.
Matrices and how they can be used in quantum computing
In this lesson, students will be introduced to the basic concepts and operations of matrices, which are essential tools in mathematics, physics, computer science and quantum computing. They will explore how matrices can be used to organise and transform data, and how they are applied in real-world quantum systems.
Using the Bloch sphere to represent a qubit
Students discover how the seemingly complex expression of a qubit can be simplified and visualised on the Bloch sphere. By reducing the state to two angles, the lesson makes quantum states intuitive and accessible for classroom exploration.
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