I’m done with the Chapter 2 - One Quantum Bit of the Introduction to Classical and Quantum Computing - Thomas Wong which was our first introduction to Qubit in this book. Instead of going through the usual Linear Algebra route to learn about the intricacies and mechanics of qubits, we took a different route, a geometric one. Let’s delve deeper.

Lessons learned

We were first introduced to a unique board game, designed by Thomas Wong himself, that utilizes the principles of quantum mechanics, Qubit Touchdown (thegamecrafter.com). We then quickly moved on to the nitty gritty details of qubits, how they are similar and dissimilar to classical bits, and how they can be represented, both mathematically (Paul Dirac Notation) and visually (Bloch sphere). We then learned about the idea of superposition and how a qubit’s state can be a combination of both $\ket 0$ and $\ket 1$.

After that, we reviewed some basic properties and formulas for complex numbers, how to represent them in different forms and convert from one form to another, which will become helpful later on when we study qubits, as their amplitudes could be complex numbers as well.

We then saw how to measurement a qubit in the $Z$-basis, and how to normalize it (such that its total probability is $1$). We also explored how to measure a qubit in any of the basis, i.e. $X$-basis, $Y$-basis, and $Z$-basis, and how measurement in different consecutive basis gives rise to some interesting properties of quantum computing. We then learned about the physical irrelevancy of global phases and physical relevancy of relative phases. We also saw how to visualize a qubit on a Bloch sphere i.e. how to write $\alpha$ and $\beta$ (amplitudes of $\ket 0$ and $\ket 1$ respectively) in terms of two angles $\theta$ and $\phi$ and vice versa.

A brief description of various physical system that can be used to represent a qubit was also given which included systems like photons, trapped ions, cold atoms, superconductors, among others. Finally we learned about quantum gates which are linear maps that act on a qubit to transform its state while keeping the total probability equal to $1$. We then learned about some of the common single-qubit gates, such as Pauli X-gate, Pauli Y-gate, Pauli Z-gate, Hadamard gate, etc. We also looked at how quantum circuits can be used to represent what quantum gates act on a qubit.

Moving forward

As I’ve told you before, I’m working on creating an automated workflow that would publish my notes from Obsidian.md whenever I make an update. Right now I’m working on modifying the Obsidian Zola theme, and I’ve made quite a progress. I’ll let you guys know when it is up and running. That way I won’t have to share my PDF notes here, and you can easily view them on that site, with more interactivity.

If you have any suggestions or questions, feel free to comment below. Talk to you tomorrow, InshaAllah.

PDF Notes

My notes on the second Chapter of the Thomas Wong’s Introduction to Classical and Quantum Computing book.

If the PDF display is not working, you can download it from here: Link