Qubit Visualizations

Table Of Contents

• What is information?
• Qubit and the Bloch Sphere
• States and the Bloch Circle
• 2-qubit states and the torus model
• Entangled states and the torus knot

Each chapter in the table of content is a web-page that can be found in the navigation bar. Jump to each section by navigating the sidebar. On tablets and mobile phones the sidebar is replaced with a menu icon to open the sidebar.

Why this tutorial?

Understanding many important concepts of quantum mechanics, such as entanglement, requires developing intuitions about states with a minimum of two qubits, which is typically introduced in advanced quantum mechanics course that requires background knowledge of advanced math or physics. This tutorial encodes quantum states, their properties and evolutions into interactive visualizations, which require only basic linear algebra and probability theory to interpret. By doing so, this tutorial may be useful for understanding fundamental concepts of quantum mechanics and quantum information at an introductory level. Details about how we obtain the visualization can be found in our paper "Geometric Visualizations of Single and Entangled Qubits".

Ackknowledgement

I would like to express my gratitude to my advisor, Prof. Paul-Cadden Zimansky, who directed me throughout this project.

The construction of this tutorial website is supported by Bard Summer Research Insitute and the Bard Physics Department.

Tufte.css , d3.js , Three.js , is adapted to create the stylings of and animations on this tutorial webpage.