Introduction to Quantum Algorithms

Quantum algorithms are among the most important, interesting, and promising innovations in information and communication technology. They pose a major threat to today's cybersecurity and at the same time promise great benefits by potentially solving previously intractable computational problems with reasonable effort. The theory of quantum algorithms is based on advanced concepts from computer science, mathematics, and physics. Introduction to Quantum Algorithms offers a mathematically precise exploration of these concepts, accessible to those with a basic mathematical university education, while also catering to more experienced readers. This comprehensive book is suitable for self-study or as a textbook for one- or two-semester introductory courses on quantum computing algorithms. Instructors can tailor their approach to emphasize theoretical understanding and proofs or practical applications of quantum algorithms, depending on the course's goals and timeframe. Contents Preface 1. Classical Computation 2. Hilbert Spaces 3. Quantum Mechanics 4. The Theory of Quantum Algorithms 5. The Algorithms of Deutsch and Simon 6. The Algorithms of Shor 7. Quantum Search and Quantum Counting 8. The HHL Algorithm Appendix A. Foundations Appendix B. Linear Algebra Appendix C. Probability Theory Appendix D. Solutions of Selected Exercises Bibliography Index