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