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Introduction to Quantum Physics and Quantum Computers

G. Ríos

Published Jun 1, 2017• 0 citations
OpenAlex

Abstract

In the first part of this science lecture we take Richard Feynman famous words about nobody understanding quantum mechanics as a challenge to be overcome a the level of a typical sophomore college students. As a second part we examine the principles of quantum computers and run Shor algorithm as an example.

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Mr Administrator,Dear colleagues,Ladies and gentlemen,“I think I can safely say that nobody understands quantum mechanics”. This statement, made by physicist Richard Feynman, expresses a paradoxical truth about the scientific theory that revolutionised our understanding of Nature and made an extraordinary contribution to our means of acting on and gaining information about the world. In this lecture, I will discuss quantum physics with you by attempting to resolve this paradox. And if I don’...
Richard Feynman's observation that quantum mechanical effects could not be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used quantum effects. This speculation appeared justified when Peter Shor described a polynomial time quantum algorithm for factoring integers. In quantum systems, the computational space increases exponentially with the size of the system which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new non-traditional programming techniques. The aim of this paper is to guide computer scientists and other non-physicists through the conceptual and notational barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to harnessing the power of quantum parallelism are explained, including Shor's algorithm, Grover's algorithm, and Hogg's algorithms. We conclude with a discussion of quantum error correction.
As quantum computers are becoming available for experiments, their enormous potential is being recognized among college communities. The goal of introducing quantum computing in college level computer science programs is becoming attractive. However, this goal comes with opportunities and challenges. of the challenges is that quantum computing appears to require substantial background in physics as well as in computer science. However, it is hard to convince students to major in these two fields. Computer Science students with a minor in physics can also be considered. Several alternative curriculum structures are possible. A non-consecutive two-course framework is proposed here. A course on Introduction to Quantum Computing may be offered to sophomore level students. This introductory course may teach fundamental ideas about quantum computing with basic concepts behind BQP (Bounded Error Quantum Polynomial) and related topics. This introductory course may be followed up by some physics courses (on related topics such as quantum mechanics) and some computer science courses. Then, a senior level course on Advanced Quantum Computing may be offered that may include some well-known algorithms (such as Shor's Algorithm for Quantum Factorization and Grover's Algorithm for Quantum Search) and their implementation and practices on some simulators (such as QuIDE from http://www.quide.eu/) or some prototype quantum processors (such as IBM's prototype quantum processors). For advanced level courses, some course materials are available from various sources (such as MIT OpenCourseWare). The greater challenge would be in teaching the introductory course mentioned earlier that motivates students towards investing time and efforts in learning quantum computing and related physics, math and computational topics. The challenges of teaching the introductory course should not be underestimated. Some flexible strategies can be suggested for this course so that the biggest challenges can be overcome. Some initial assessments of the students may help adjusting the introduction strategies with student's preparation. What is recommended is that the instructor should be able to adjust the coverage of topics, rigor and depth of treatment. That is, the introductory course should not be rigidly defined. It should be recognized that the main emphasis of the introductory course is actually instilling motivations and curiosity in student's mind about potentials of quantum computing through adaptive teaching of some selected topics where traditional digital computers do not provide tractable solutions. Ideally a balance could be achieved among aspects of depth of treatment, rigor, inspiration, motivation and coverage of topics. Students should be able to realize that the emerging quantum computing technology would be able to provide elegant solutions to some of the classical intractable problems combining ideas from physics, math and computer science in an innovative way. One size fits all is not a good approach and discussion of issues may help us face the challenges better by pragmatically considering a range of possible alternatives. Resources that are currently available may also need to be reviewed for the purpose of introducing quantum computing adequately.
The goal of this talk is to present an introduction to quantum computing for non-specialists. I will first present the quantum computing model in order to have a first feel of what we can and cannot do with a quantum computer. Then I will present a few iconic quantum algorithms such as Grover’s algorithm and Shor’s algorithm. Finally, I will talk about perspectives relative to quantum-secure cryptography. During the talk, I will also briefly talk about error correction for quantum computation and quantum cryptography.