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 required by the institution. 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 believe that true innovation is born at the intersection of multiple 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 fusion 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. 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 an arcane field due to the large number of prerequisites. But 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 the 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, 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 section 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’ subsection in each section to expand your knowledge and deepen your understanding, since learning is not always linear but more often network-like.

The way to understanding quantum computing and its applications will not be easy. You, as a reader, will encounter a lot of obstacles, like vague concepts that do not make sense and complex problems that look impossible to break down at first glance. But with enough dedication, effort, and resources you have, it will eventually get you through. Once you make it, you will feel more accessible to cutting-edge papers from the field of your interest than ever. Even if you end up choosing a different career path other than quantum computing, you will be able to apply some of the knowledge and skills you gained from here. I hope you enjoy it!

— Daniel Park