Calculating with quanta: Quantum computer for the curious (essentials)

45 Pages·2022·6.604 MB·English

by  Beatrice Marie Ellerhoff

Beatrice Marie Ellerhoff
Calculating with
quanta
Quantum computer for the curious
essentials
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Beatrice Marie Ellerhoff
Calculating with quanta
Quantum computer for the curious
Beatrice Marie Ellerhoff
Department of Physics and Department
of Geosciences, Tübingen Universtiy
Tübingen, Baden-Württemberg, Germany
ISSN 2197-6708 ISSN 2197-6716 (electronic)
essentials
ISBN 978-3-658-36750-3 ISBN 978-3-658-36751-0 (eBook)
https://doi.org/10.1007/978-3-658-36751-0
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Fachmedien
Wiesbaden GmbH, part of Springer Nature 2022
This book is a translation of the original German edition „Mit Quanten rechnen“ by Ellerhoff,
Beatrice Marie, published by Springer Fachmedien Wiesbaden GmbH in 2020. The translation
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Preface
The phenomena of quantum mechanics fascinate not only the research world but
increasingly also the general public. The bizarre properties of the tiny building
blocks of our matter, called quanta, arouse widespread curiosity: Harnessing quan-
tum properties for computation has the potential to provide quantum computers
with computing power exponentially faster than the best high-performance com-
puters of our time. As a result, their development is of great importance to research,
industry, and society. This book explores the quantum phenomena of entanglement
and superposition and explains how they can be used for calculations. It aims to
provide a clear, lively, and descriptive understanding of the processes involved in
quantum computing. Starting with the basic encoding of information, through the
explanation of simple algorithms, to possible applications, I look forward to guid-
ing curious readers through the world of quantum computing. This little book is
dedicated to my father, who sparked a curiosity for science in me. As a young re-
searcher, I am grateful to be given the chance to pass on this enthusiasm, and I
thank all those who contributed with their support. My special thanks go to Tim
Ellerhoff for his loving support, and to Abra Ganz, Amelie Scupin, Bruno Faigle-
Cedzich, Christopher Lance, Shirin Ermis, and Uli Schünemann for their thorough
and critical reading of the text.
Heidelberg, Germany Beatrice Marie Ellerhoff
January 2022
v
What You Can Find in This essential
• How quantum computers work
• An illustrative explanation of quantum entanglement
• How quantum particles can be used for computing
• Derivations and simple explanations of quantum algorithms
• The approaches to and significance of quantum error correction
• Current challenges and potential applications of quantum computers
vii
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Quantum Revolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Quantum Mechanics in Our Everyday Life . . . . . . . . . . . . . . . . . . . . . 3
2.2 Towards Unimaginable Computing Power . . . . . . . . . . . . . . . . . . . . . . 6
3 The Basic Building Blocks of Quantum Computing . . . . . . . . . . . . . . . . . 9
3.1 From Bits to Quantum Bits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2 Quantum Advantage Through Entanglement . . . . . . . . . . . . . . . . . . . .12
3.3 Quantum Gates and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
4 Quantum Computing Today and Tomorrow . . . . . . . . . . . . . . . . . . . . . . .21
4.1 The Search for the Optimal Hardware . . . . . . . . . . . . . . . . . . . . . . . . .21
4.2 The Decoherence Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
4.3 The Future of Quantum Computing . . . . . . . . . . . . . . . . . . . . . . . . . . .29
5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
What You Learned from This essentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .35
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .37
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39
ix
About the Author
Beatrice Marie Ellerhoff is a PhD student at the Insti-
tute of Environmental Physics in Heidelberg and at the
Geo- and Environmental Research Center (GUZ) in
Tübingen, Germany. During her studies in physics at
Heidelberg University, she wrote for the blog www.ma-
nybodyphysics.com and the Science Notes magazine.
She worked for 4 years as a student assistant at the Max
Planck Institute for Medical Research, including in the
group of Nobel Prize winner Stefan Hell. In her master’s
thesis, she investigated the entanglement of many ultra-
cold quantum particles. As part of her doctorate, Beatrice
Photo: Ute von Figura
Ellerhoff is now turning her attention to the macroscopi-
cally tangible world and researching the fundamentals of
climate fluctuations on long time scales in Kira Rehfeld’s
group. She is particularly fascinated by the linkage of
physical concepts across disciplines. In addition to re-
search, she is passionate about running and jazz piano.
She was a fellow of the Heidelberg Graduate School for
Fundamental Physics and receives a doctoral scholarship
from the Heinrich-Böll-Stiftung.
Beatrice Marie Ellerhoff, Geo- and Environmen-
tal Research Center (GUZ), Schnarrenbergstr. 94-96,
72076 Tübingen, Germany.
xi
Introduction 1
From a physics perspective, quantum mechanics has shaped the past century. In
addition to Albert Einstein’s general theory of relativity, it was the quantum theory
that has led to a paradigm shift in the way we look at the laws of nature. Ever since
Niels Bohr presented the first atomic model with quantum mechanical properties in
1913, physicists have been describing the world of the smallest particles using the
language of quantum mechanics. In this context, energy and momentum are not
continuous, but restricted to discrete “quantized” values. Quantum mechanics goes
even further, as it describes not only radiation but also matter as waves.
The modern quantum mechanics created the basis for a multitude of new
achievements. It was an astonishingly short path from the discovery of the funda-
mental principles to their first applications, such as the laser. Now another “quan-
tum leap” is in sight: Quanta will be used to process information and to enable
unprecedented computing power. Quantum computers could outperform today’s
supercomputers by far and thus answer unsolved questions, for example in the field
of drug development. Numerous research groups and companies are working in-
tensively to bring quantum computing out of its infancy and promise new insights
for many areas of industry and research.
© The Author(s), under exclusive license to Springer Fachmedien 1
Wiesbaden GmbH, part of Springer Nature 2022
B. M. Ellerhoff, Calculating with quanta, essentials,
https://doi.org/10.1007/978-3-658-36751-0_1