Solved Problems in Quantum Physics

Jaroslav Kafka

Title: Solved Problems in Quantum Physics - angular momentum and spin Author: Jaroslav Kafka Department: Department of Physics Education Supervisor: RNDr. Zdeňka Koupilová, Ph.D., Department of Physics Education Abstract: The aim of this bachelor thesis was to create a set of solved problems in quantum physics for the electronic Collection of Solved Problems in Physics. Within this thesis 18 problems were created, which belong to the chapter Microworld Physics, mostly at the undergraduate level. There is described a brief history of the electronic collection and its technical background in the context of the user and the administrator. Part of the thesis includes description of the tasks in the matter of physical issues and its interconnection with other tasks of the Collection of Solved Problems in Physics. In the appendix there are presented selected solved problems with structured sollution. All tasks can be found on the website http://reseneulohy.cz/ or on the attached CD. Keywords: electronic collection, solved problems, quantum physics 1

Leonardo Angelini

Z. Ficek

This book contains tutorial problems with solutions for the textbook Quantum Physics for Beginners. The reader studying the abstract field of quantum physics needs to solve plenty of practical, especially quantitative, problems. This book places emphasis on basic problems of quantum physics together with some instructive, simulating, and useful applications. A considerable range of complexity is presented by these problems, and not too many of them can be solved using formulas alone.

Emilio d’Emilio, Luigi E. Picasso

Emilio d’Emilio, Luigi E. Picasso

Elijah Pelofske, Georg Hahn, Hristo N. Djidjev

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.