This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing discipline and find themselves taken aback by the language gap between mathematics and the pioneering fields on the matter: computer science and quantum physics. A first version of this paper was originally published at arXiv in October 2018. Minor corrections added on Spring 2025.
This paper is an essentially self-contained and rigorous description of the fundamental principles of quantum computing from a mathematical perspective. It is intended to help mathematicians who want to get a grasp of this quickly growing discipline and find themselves taken aback by the language gap between mathematics and the pioneering fields on the matter: computer science and quantum physics. A first version of this paper was originally published at arXiv in October 2018. Minor corrections added on Spring 2025.
With its potential to completely change computation, quantum computing—a groundbreaking discipline that sprung from computer science and quantum mechanics—has attracted a lot of interest. This essay attempts to cover the foundations of quantum computing and offer a thorough manual for readers who are not specialists in the subject. We start by going over the basic ideas of quantum computing and then take readers through the concepts of qubits, superposition, entanglement, interference, and noise. We study quantum gates, quantum hardware, and fundamental quantum circuits. This paper provides an overview of the present state of quantum computing, focusing on the noisy intermediate-scale quantum (NISQ) era and its possible applications to practical issues. delve into the creation of quantum algorithms and their uses, emphasizing well-known algorithms like as Grover's and Shor's. We also discuss how several fields, like material science, machine learning, encryption, and optimization, are affected by quantum computing. Upon finishing this paper, readers will possess a firm grasp of the fundamentals, practical uses, and procedures of quantum circuit development. Our objective is to offer an invaluable resource for scholars hoping to keep current on this quickly developing topic as well as for those ready to start their adventure with quantum computing
The theory of quantum computation is presented in a self contained way from a computer science perspective. The basics of classical computation and quantum mechanics is reviewed. The circuit model of quantum computation is presented in detail. Throughout there is an emphasis on the physical as well as the abstract aspects of computation and the interplay between them. This report is presented as a Master's thesis at the department of Computer Science and Engineering at G{ö}teborg University, G{ö}teborg, Sweden. The text is part of a larger work that is planned to include chapters on quantum algorithms, the quantum Turing machine model and abstract approaches to quantum computation.
In this article, we present an introduction to quantum computing (QC) tailored for computing professionals such as programmers, machine learning engineers, and data scientists. Our approach abstracts away the physics underlying QC, which can be challenging to grasp, and frames it as a model of computation similar to, for instance, Turing machines. This helps readers grasp the fundamental principles of QC from a purely logical perspective. We begin by defining quantum states and qubits, establishing their mathematical representation and role in computation. We introduce fundamental concepts such as basis states, quantum gates, and tensor products, illustrating how these form the building blocks of quantum computation. Then we present the Deutsch-Josza algorithm, one of the simplest quantum algorithms that demonstrate how quantum computers can outperform classical computers. Finally, we provide guidance for further study, recommending resources for those interested in exploring quantum algorithms, implementations, and industry applications.
A self-contained treatment of the fundamentals of quantum computing
This clear, practical book takes quantum computing out of the realm of theoretical physics and teaches the fundamentals of the field to students and professionals who have not had training in quantum computing or quantum information theory, including computer scientists, programmers, electrical engineers, mathematicians, physics students, and chemists. The author cuts through the conventions of typical jargon-laden physics books and instead presents the material through his unique how-to approach and friendly, conversational style.
Readers will learn how to carry out calculations with explicit details and will gain a fundamental grasp of:
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Quantum mechanics
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Quantum computation
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Teleportation
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Quantum cryptography
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Entanglement
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Quantum algorithms
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Error correction
A number of worked examples are included so readers can see how quantum computing is done with their own eyes, while answers to similar end-of-chapter problems are provided for readers to check their own work as they learn to master the information.
Ideal for professionals and graduate-level students alike, Quantum Computing Explained delivers the fundamentals of quantum computing readers need to be able to understand current research papers and go on to study more advanced quantum texts.
This book provides an easy-to-read but practical introduction to quantum gate simulation to serious learners of the subject. Fundamental physical concepts and selected programming examples of quantum simulations are described for readers who want to use the simulation with a physical understanding background without the use of rigorous mathematics. This book is intended to offer a self-study book for senior and graduate students of physics, computer science, and mathematics who want to learn and write quantum codes. It may also serve as a textbook or a reference in academia and industry. Readers are expected to have introductory knowledge of linear algebra although it is briefly reviewed in this book. Some experience of computer programming is helpful, but no prior knowledge of Python is required for writing the quantum codes shown in this book. Part of IOP Series in Quantum Technology. Key features • Easy-to-read content for self-paced readers. • Many examples with background physics. • Detailed description of entanglement and teleportation. • Guide to industrial resources. • DIY quantum gate simulations.