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Quantum computation is one of those topics that never ceases to intrigue. It ’ s an intellectual puzzle, a practical tool, and a glimpse into what might just be the future of computing. Teaching this subject at Fudan University for a one-semester course, I ’ ve seen firsthand how students ’ eyes light up when they begin to grasp the strange, beautiful logic of quantum mechanics. Yet diving into quantum computation can feel like jumping into an ocean without knowing how to swim. The field is vast and complex, and many textbooks on the subject seem determined to cover everything under the sun. That ’ s why I decided to write “ Quantum Computing Unveiled: A Concise Course with Topological Extensions. ” I wanted to create a book that provides a solid grounding without overwhelming you with information. The idea was simple: Cover what ’ s essential and make it accessible within the span of a single semester. A book that doesn ’ t just sit on the shelf, collecting dust, but one that can be actively used in a classroom. And not just for the experts but for graduate and advanced undergraduate students eager to explore this fascinating field. Now, I must admit, I couldn ’ t resist adding a bit of my personal touch. There ’ s a chapter on topological quantum computing, a subject I find fascinating. Before we dive into that, though, we explore topological orders and surface codes. It ’ s essential to understand these underlying concepts, as they pave the way for the innovative thinking that topological quantum computing represents. These chapters are more than a sequential progression; they ’ re a logical unfolding of ideas, one leading naturally into the other, offering a cohesive understanding of a complex subject. Teaching quantum computation is a bit like leading an expedition into uncharted territory. There are familiar landmarks, unexpected obstacles, and plenty of opportunities for discovery. In this book, I ’ ve tried to lay out a clear path, starting with the foundational concepts and gradually building up to more complex topics like quantum algorithms, error correction, and yes, topological quantum computing. Along the way, I ’ ve done my best to keep things engaging. Quantum computation shouldn ’ t be a dry, abstract subject. It ’ s filled with surprising insights, puzzling paradoxes, and practical applications that could change the world. I ’ ve tried to capture some of that excitement in these pages. I know that quantum computation can be daunting. I ’ ve seen students struggle with the material, wrestle with the concepts, and then suddenly have that “ aha ” moment when it all clicks. That ’ s what I hope to achieve with this book – a guide that doesn ’ t just tell you about quantum computation but helps you understand it, question it, and may even fall in love with it, just a little bit. So here it is, “ Quantum Computation Unveiled: A Concise Course with Topological Extensions. ” While quantum information, particularly quantum communication and cryptography, often appears in books on quantum computation, this text will not address these topics. First, quantum computation is both a subset and an application of quantum information theory, emphasizing the effective manipulation of quantum information. Second, key aspects of quantum information theory, such as quantum error correction and quantum decoherence, will be covered in the context of constructing quantum computers. Additionally, quantum information is an extensively developed field with numerous branches, each deserving comprehensive treatment in its own right. Covering all these areas would require an entire book for each branch, making it reasonable to focus this work specifically on quantum computation. Maintaining a clear focus on quantum computation ensures a more coherent narrative and avoids diluting the core subject with material that, though related, is vast and adequately covered elsewhere. This being a concise book, instructions for its use are straightforward: For a 14- to 16-week course, three 45-minute lectures per week, the entire book can be covered. For shorter courses, chapters can be selected accordingly. If students are already well versed in quantum mechanics, Chapter 3 can be skipped. For those with a computer science background, Chapter 2 may be unnecessary. If the course aims to provide a primer on quantum computation, Chapters 8 and 9 , which cover surface codes and topological quantum computation, may be beyond its scope. In the case of a single-quarter course, Chapters 2 , 3 , 8 , and 9 can all be omitted.