Introduction
Whether meeting a new person or learnign a new concept, everyone needs an introduction, and a book like this one is no exception. This chapter is a gentle introduction to this textbook and quantum computing. To use this text effectively, read this chapter before moving on to specific topics.
Chapter Contents
Preface
I was a typical university student at Rensselaer Polytechnic Institute studying computer science and mathematics. The vast majority of people who are not in STEM would see computer science and mathematics as identical fields, which is understandable, but their approaches to discovering truth are quite different. A mathematician would enjoy the elegance of refined abstract ideas, rigorous logic, and creative solutions; on the other hand, a computer scientist would focus on more ‘practical’ problems that mathematicians may not care about. A mathematician may also criticize computer scientists for lax mathematical rigor, while a computer scientist may condemn mathematicians for solving problems with no practical use.
There was an ambiguous yet confident belief inside me, which motivated me to major in both subjects despite the heavy workload. The belief was that, even though each field offers a different worldview, they do not have to be in conflict. I was aware that both computer science and mathematics play vital roles in our lives in their own ways. Furthermore, I believed that true innovation is born at the intersection of multiples disciplines, achieved through consistent communication and drawing inspiration from diverse perspectives. I called this belief ‘ambiguous’ simply because I could not name any solid example at that time.
It was my sophomore year to discover the existence of quantum computing, and it did not take long for me to realize that it was direct evidence of my belief. Quantum computing is the harmony of mathematics, computer science, quantum mechanics, and last but not least, engineering. Mathematics provides the formal backbone for quantum mechanics; quantum mechanics explains the ‘unusual’ rules of the microscopic world; computer science describes how these rules can benefit computation; and engineering turns quantum computers from theory into reality. Also, as this text will address, quantum computing promises to bring advantages to many research fields, not limited to the disciplines mentioned earlier.
Many people assume that quantum computing is arcane due to the large number of prerequisites; my ambition for this project is to make quantum computing accessible to everyone. We must acknowledge that some readers prefer rigor while others prefer intuition; to make this text truly accessible to everyone, I must balance these values When I propose a rigorous definition, I will provide intuitive examples to make it comprehensive and approachable. Not forgetting the practical side, I plan to include chapters on applications of quantum computing after the theory part.
I initially started this project to archive what I learned from quantum computing courses at university. Soon I realized that the best way to learn is to teach, as it forces me to organize information and find intuition in abstract ideas. As a recent graduate, I must admit that I do not possess enough knowledge or experience to ensure factual accuracy throughout the text. I addressed this by making the project open source, which enables bidirectional communication between the author and readers, allowing the text to be consistently updated based on feedback.
I expect this text will be accessible to anyone familiar with high school algebra and trigonometry. However, some topics may require graduate-level knowledge, so I highly recommend consulting the Chapter Dependency page before diving into a specific topic. In addition, please understand that practice problems may not be available given the breadth of material covered. To avoid gaps in understanding, be sure to consult the ‘Further Reading’ section on each page to expand your knowledge and deepen your understanding, since learning is not always linear but more often network-like.
There are many paths to reach the top of a mountain. People with different preferences take different paths that lead to the same goal. At the top of the mountain, people share what they observed during the climb, and disagreements may arise. I hope this text becomes a guide that helps everyone appreciate the landscape of each discipline, so that we can better understand one another, as human beings.
— Daniel Park
Acknowledgements
This page recognizes any individuals who have contributed to the development and enrichment of this textbook. Contributors of this project are listed with their permission. Additional sources, such as books, articles, and papers, are referenced in the ‘Further Reading’ section of each chapter. I sincerely appreciate your dedication and continued support.
Project Leaders
Project leaders guide the direction of the project, making key decisions and facilitate a collaborative community. They are responsible for reviewing pull requests, ensuring proper grammar, factual accuracy, consistent language, and appropriate use of external resources.
- Daniel Park (Luxque): Main author.
Content Contributors
Content contributos are individuals who have generously shared their original concepts, algorithms, advice, and/or peadagogical approaches featured in this textbook. Their insights enhance the content and inspire new perspective on quantum computing and quantum algorithms. Each contributor is acknowledged with their permission.
Translators
Translators play a vital role in making knowledge accessible to a global audience. Their support helps to overcome language barriers and ensure that this textbook reaches as many readers as possible. Each translator is acknowledged with their permission.
Reviewers
A top-notch textbook must aim for accuracy and clarity. Error reviewers assist by fact-checking, identifying missing sources, and pointing out conceptual/typographical errors from the text. Their valuable contributions help maintaining the integrity of the content. Each reviewer is acknowledged by their permission.
Donators
Donations support the ongoing development of this project and enable the acquisition of valuable resources. Every donation is highly appreciated. While it may be challenging to maintain a comprehensive list of donors, I will make best effort to update it as frequently as possible.
Last Updated: 12/13/2025
Notations
This page provides a brief overview of notational conventions that will be used in this book. Please note that this page does not provide a detailed explanation of what each symbol represents. Readers can use the search tool at the top of the page to find detailed explanations and relevant concepts.
Mathematical Symbols
This table serves as a reference for the mathematical symbols that will be used throughout this text. Precise definitions are not yet provided here but will be introduced as the material progresses. Even if you are already familiar with these notations, it is still highly recommended to review this section, as different texts may employ varying conventions and symbol choices.
Please note that some mathematical symbols closely resemble Greek letters commonly used as variable names. One notable example would be \(\sum\) and \(\Sigma\); the former represents the summation operator, while the latter may be used as a variable name (e.g., for a set or a matrix). Readers should be able to distinguish these symbols by context.
| Symbol | Description |
|---|---|
| \(\sum\) | summation |
| \(\prod\) | product |
| \(\oplus\) | bitwise XOR operation |
| \(\otimes\) | tensor product |
Greek Alphabet
In mathematics, science, and engineering, a wide range of variables and constants are notated by Greek alphabet. Readers are encouraged to consult this table and become familiar with the shapes and names of these letters, as they will appear throughout the text. In most cases, a Greek letter is chosen when the name of the variable can be phonetically associated with that letter.
Please note that some Greek letters have multiple forms that share the same name, particularly in text typeset with \(\LaTeX\). One common example would be \(\phi\) and \(\varphi\); although both are often referred to as ‘phi’ in everyday use, they have distinct shapes. Unless specified, this textbook will treat such variants as separate symbols. Consistent use of each form will be maintained in order to avoid any unnecessary confusion.
| Uppercase | Lowercase | Name |
|---|---|---|
| Α | α | alpha |
| Β | β | beta |
| Γ | γ | gamma |
| Δ | δ | delta |
| Ε | ε | epsilon |
| Ζ | ζ | zeta |
| Η | η | eta |
| Θ | θ | theta |
| Ι | ι | iota |
| Κ | κ | kappa |
| Λ | λ | lambda |
| Μ | μ | mu |
| Ν | ν | nu |
| Ξ | ξ | xi |
| Ο | ο | omicron |
| Π | π | pi |
| Ρ | ρ | rho |
| Σ | σ, ς | sigma |
| Τ | τ | tau |
| Υ | υ | upsilon |
| Φ | φ | phi |
| Χ | χ | chi |
| Ψ | ψ | psi |
| Ω | ω | omega |
Chapter Dependency
This page provides a convenient guide to the prerequisites for each chapter. Please note that the most efficient way to learn a topic may not be linear due to the variety of subjects covered in this text. Readers can find topics of interest in the table of contents and use this guide to trace back prereqiusite chapters.
Chapter 1: Introduction
This chapter has no prerequisites.