Название: Quantum Computing and Quantum Physics: A Linear Algebra Approach
Автор: Alice Flarend, Robert Hilborn
Издательство: Oxford University Press
Год: 2026
Страниц: 488
Язык: английский
Формат: pdf (true)
Размер: 14.1 MB

Quantum Computing and Quantum Physics: A Linear Algebra Approach provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The book is designed for undergraduate students with little or no background in physics but with some familiarity with linear algebra. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide ranging backgrounds will also find the book useful and enjoyable. While broadly accessible, the book does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement—the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when quantum computing has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers and help them digest the many counterintuitive quantum information science and quantum computing concepts. Self-contained chapters on time dependence in quantum mechanics, magnetic resonance, density matrices, simple harmonic oscillator, quantum perturbation theory, and number operators provide a basis for further reading and work in quantum information science and quantum computing.

We are finally ready to tackle some actual quantum computing algorithms. As shown later, quantum computing algorithms are not just classical computing algorithms modified to run on a quantum computer. Quantum algorithms are new ways of thinking about problems and are designed to exploit the properties of quantum states, quantum gates, and measurement devices.

We start with a few of the standard quantum algorithms, which were invented decades ago, primarily to show how we can use the features of quantum states, particularly entangled states, to implement algorithms more quickly or more efficiently than we can with classical computers. Many of these algorithms are, in a sense, designed to solve “made up” problems—problems selected because they are amenable to quantum algorithms and show some “advantage” over classical computational algorithms. There are many slightly different versions of these algorithms. We use versions that are fairly simple to understand.

In some ways, the current state of quantum algorithms is what classical computer programming was like before high-level languages such as Fortran, C, Python, and so on were developed. We are sure that within a decade or so, we will have similar high-level languages for quantum computing. For the short-term future, it is highly likely that the commands you send to a quantum computer will be specific for each device because you need to communicate directly with that device’s hardware. Most browser-accessible quantum computer systems provide you with a commonly available programming language such as Python with special instructions in another layer you do not see that handle the direct communications with the hardware. Eventually higher-level quantum programming languages will be developed akin to Python or C# running on classical computers; so, the typical user will not need to worry at all about how to communicate with the specific underlying hardware.