Natural computing / Quantum computing Books

Book SynopsisThe ultimate non-technical guide to the fast-developing world of quantum computing Computer technology has improved exponentially over the last 50 years. But the headroom for bigger and better electronic solutions is running out. Our best hope is to engage the power of quantum physics. 'Quantum algorithms' had already been written long before hardware was built. These would enable, for example, a quantum computer to exponentially speed up an information search, or to crack the mathematical trick behind internet security. However, making a quantum computer is incredibly difficult. Despite hundreds of laboratories around the world working on them, we are only just seeing them come close to 'supremacy' where they can outperform a traditional computer. In this approachable introduction, Brian Clegg explains algorithms and their quantum counterparts, explores the physical building blocks and quantum weirdness necessary to make a quantum computer, and uncovers the capabilities of the current generation of machines.Trade ReviewEssential reading for anyone concerned about cyber attacks, specifically ransomware, or simply interested in the next evolution of computing. The big question - what is a Quantum Machine - is answered perfectly. ... [E]xcellently profiles the different quantum approaches ... and readers are made aware of the extreme potential of the Qubit Revolution to support the next evolution of humanity and civilisation. -- Nick Ayton * Irish Tech News *

Read more less

Book SynopsisA distinctive and accessible introduction to quantum information science and quantum computing, this textbook provides a solid conceptual and formal understanding of quantum states and entanglement for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics.Trade ReviewWhile broadly accessible, the textbook 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 QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *This is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *This is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *The reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *Table of Contents1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC

Read more less

Book SynopsisQuantum Computing: From Alice to Bob provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The textbook is designed for undergraduate students and upper-level secondary school students with little or no background in physics, computer science, or mathematics beyond secondary school algebra and a bit of trigonometry. 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 textbook 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 QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts.Trade ReviewWhile broadly accessible, the textbook 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 QC has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers in problem solving (both with and without mathematics) and help them digest the many counter-intuitive quantum information science and quantum computing concepts. * zb Math Open *This is a refreshing, pedagogical, and timely overview of quantum computing for non-experts, by two well-qualified authors. * Shimon Kolkowitz, University of Wisconsin-Madison *This is a much needed bridge between popular and technical texts that provides easy access to the topic of quantum computing for curious readers who aim to go further and deeper in their understanding. * Dieter Jaksch, University of Oxford *The reader gets to avoid the complexity of technical quantum-computing books, yet gets more depth and rigor than in the popular writing on the topic...the book is written in a very conversational rather than academic tone. * Bogdan Hoanca, University of Alaska Anchorage *Table of Contents1: Introduction 2: Traditional Computing 3: Traditional Bits in New Clothes 4: Qubits and Quantum States 5: Quantum Measurements 6: Quantum Gates 7: Putting a Spin on Spin 8: My Basis, Your Basis 9: Multi-qubit Systems, Entanglement, and Quantum Weirdness 10: Quantum Circuits and Multi-qubit Applications 11: Quantum Computing Algorithms 12: More Quantum Algorithms 13: RSA Encryption and the Shor Factoring Algorithm 14: Fundamental Quantum Issues 15: Complexifying Quantum States 16: Present and Future QIS and QC

Read more less

Book SynopsisThis new book discusses the concepts while also highlighting the challenges in thefield of quantum cryptography and also covering cryptographic techniques and cybersecurity techniques, in a single volume.It comprehensively covers important topics in the field of quantum cryptographywith applications, including quantum key distribution, position-based quantumcryptography, quantum teleportation, quantum e-commerce, quantum cloning, cybersecurity techniques' architectures and design, cyber security techniques management,software-defined networks, and cyber security techniques for 5G communication.The text also discusses the security of practical quantum key distribution systems,applications and algorithms developed for quantum cryptography, as well as cybersecurity through quantum computing and quantum cryptography.The text will be beneficial for graduate students, academic researchers, andprofeTable of Contents1. Towards Security in Software Defined Networks with Trust and Monitoring 2. Quantum key generation and distribution using Decoy state 3. Cyber Security Techniques, Architectures and Design 4. Secured Unmanned Aerial Vehicle based Fog Computing Network (UAV-FCN): A Review 5. Mars Surface Exploration via Unmanned Aerial Vehicles: Secured MarSE UAV Prototype 6. Quantum Cryptography in Cybersecurity: A Holistic Approach 7. Cyber Security Technique for Internet of Things using Machine Learning 8. Image Encryption and Decryption through Quantum Cryptography 9. Cyber Security Techniques Management 10. Quantum Cryptography And Quantum Key Distribution 11. Quantum Cryptography: Basics, Effects on Communication and Data Management 12. Quantum Number: An Error Correction Circuits and Methods 13. Risk Analysis Assessment of Inter-Dependency of Vulnerabilities In Cyber-Physical Systems

Read more less

Book SynopsisThis pocket guide provides software developers with a quick reference to Qiskit, an open source SDK for working with quantum computers. Packed with helpful programming examples, tables, figures, and lists, this handy book helps you find the information you need to develop and debug quantum programs.

Read more less

Book SynopsisLearn Quantum Computing with Python and Q# demystifies quantum computing. Using Python and the new quantum programming language Q#, you’ll learn QC fundamentals as you apply quantum programming techniques to real-world examples including cryptography and chemical analysis. Learn Quantum Computing with Python and Q# builds your understanding of quantum computers, using Microsoft’s Quantum Development Kit to abstract away the mathematical complexities. You’ll learn QC basics as you create your own quantum simulator in Python, then move on to using the QDK and the new Q# language for writing and running algorithms very different to those found in classical computing. Key Features · The underlying mechanics of how quantum computers work · How to simulate qubits in Python · Q# and the Microsoft Quantum Developer Kit · How to apply quantum algorithms to real-world examples For readers with basic programming skills and some experience of linear algebra, calculus and complex numbers. About the technology Quantum computing is the next step in computing power and scalability, with the potential to impact everything from data science to information security. Using qubits, the fundamental unit of quantum information, quantum computers can solve problems beyond the scale of classical computing. Software packages like Microsoft's Quantum Development Kit and the Q# language are now emerging to give programmers a quick path to exploring quantum development for the first time. Christopher Granade completed his PhD in physics (quantum information) at the University of Waterloo’s Institute for Quantum Computing, and now works in the Quantum Architectures and Computation (QuArC) group at Microsoft. He works in developing the standard libraries for Q# and is an expert in the statistical characterization of quantum devices from classical data. Previously, Christopher helped Scott Aaronson prepare lectures into his recent book, Quantum Computing Since Democritus. Sarah Kaiser completed her PhD in physics (quantum information) at the University of Waterloo’s Institute for Quantum Computing. She has spent much of her career developing new quantum hardware in the lab, from satellites to hacking quantum cryptography hardware. Communicating what is so exciting about quantum is her passion, and she loves finding new demos and tools to help enable the quantum community to grow. When not at the keyboard, she loves kayaking and writing books about engineering for kids.

Read more less

Book SynopsisThe amalgamation of post-quantum cryptography in cyber-physical systems makes the computing system secure and also generates opportunities in areas like smart contracts, quantum blockchain, and smart security solutions. Sooner or later, all computing and security systems are going to adopt quantum-proof cryptography to safeguard these systems from quantum attacks. Post-quantum cryptography has tremendous potential in various domains and must be researched and explored further to be utilized successfully. Advancements in Quantum Blockchain With Real-Time Applications considers various concepts of computing such as quantum computing, post-quantum cryptography, quantum attack-resistant blockchain, quantum blockchains, and multidisciplinary applications and real-world use cases. The book also discusses solutions to various real-world problems within the industry. Covering key topics such as cybersecurity, data management, and smart society, this reference work is ideal for computer scientists, industry professionals, academicians, practitioners, scholars, researchers, instructors, and students.

Read more less

Book SynopsisThe revolution is here. In breakthrough after breakthrough, pioneering physicists are unlocking a new quantum universe which provides a better representation of reality than our everyday experiences and common sense ever could. The birth of quantum computers - which, like Schrödinger's famous dead-and-alive cat, rely on entities like electrons existing in a mixture of states - is starting to turn the computing world on its head.In his fascinating study of this cutting-edge technology (first published as Computing with Quantum Cats and now featuring a new foreword), John Gribbin updates his previous views on the nature of quantum reality, arguing for a universe of many parallel worlds where 'everything is real'. Looking back to Alan Turing's work on the Enigma machine and the first electronic computer, Gribbin explains how quantum theory developed to make quantum computers work in practice as well as in principle. He takes us beyond the arena of theoretical physics to explore their practical applications - from machines which learn through 'intuition' and trial and error to unhackable laptops and smartphones. And he investigates the potential for this extraordinary science to allow communication faster than light and even teleportation, as we step into a world of infinite possibility.

Read more less

Book SynopsisThis book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future.Table of ContentsChapter 1: Superposition.- Chapter 2: Quantization.- Chapter 3: Spin.- Chapter 4: Qubits.- Chapter 5: Entanglement.- Chapter 6: Quantum Key Distribution.- Chapter 7: Quantum Gates.- Chapter 8: Teleportation.- Chapter 10: Computational Complexity.- Chapter 11: Deutsch Algorithm.- Chapter 12: Grover Algorithm.- Chapter 13: Shor Algorithm.- Chapter 14: Physical Implementation of Single-Qubit Gates.- Chapter 15: Electron Spin Resonance.- Chapter 16: Two-state Dynamics.- Chapter 17: Physical Implementation of Two-qubit Gates.- Chapter 18: DiVincenzo Criteria.- Chapter 19: Nuclear Magnetic Resonance.- Chapter 20: Solid-state Spin Qubits.- Chapter 21: Trapped Ion Quantum Computing.- Chapter 22: Superconducting Qubits.- Chapter 23: Adiabatic Quantum Computing.- Chapter 24: Optical Quantum Computing.- Chapter 25: Quantum Error Correction.- Chapter 26: Topological Quantum Computing.

Read more less

Book SynopsisThis textbook introduces the non-specialist reader to the concepts of quantum key distribution and presents an overview of state-of-the-art quantum communication protocols and applications. The field of quantum cryptography has advanced rapidly in the previous years, not least because with the age of quantum computing drawing closer, traditional encryption methods are at risk.The textbook presents the necessary mathematical tools without assuming much background, making it accessible to readers without experience in quantum information theory. In particular, the topic of classical and quantum entropies is presented in great detail. Furthermore, the author discusses the different types of quantum key distribution protocols and explains several tools for proving the security of these protocols. In addition, a number of applications of quantum key distribution are discussed, demonstrating its value to state-of-the-art cryptography and communication. This book leads the reader through the mathematical background with a variety of worked-out examples and exercises. It is primarily targeted at graduate students and advanced undergraduates in theoretical physics. The presented material is largely self-contained and only basic knowledge in quantum mechanics and linear algebra is required.Table of Contents

Read more less

Book SynopsisThis book integrates the foundations of quantum computing with a hands-on coding approach to this emerging field; it is the first to bring these elements together in an updated manner. This work is suitable for both academic coursework and corporate technical training.The second edition includes extensive updates and revisions, both to textual content and to the code. Sections have been added on quantum machine learning, quantum error correction, Dirac notation and more. This new edition benefits from the input of the many faculty, students, corporate engineering teams, and independent readers who have used the first edition.This volume comprises three books under one cover: Part I outlines the necessary foundations of quantum computing and quantum circuits. Part II walks through the canon of quantum computing algorithms and provides code on a range of quantum computing methods in current use. Part III covers the mathematical toolkit required to master quantum computing. Additional resources include a table of operators and circuit elements and a companion GitHub site providing code and updates.Jack D. Hidary is a research scientist in quantum computing and in AI at Alphabet X, formerly Google X. Trade Review“This well-put-together book is a valuable addition to the literature in the field.” (Shrisha Rao, Computing Reviews, February 3, 2023)Table of Contents-Preface the the Second Edition.- Preface to the First Edition.- Acknowledgements.- Navigating this Book.- I. Foundations.- 1. Superposition, Entanglement and Reversibility.- 2. A Brief History of Quantum Computing.- 3. Qubits, Operators and Measurement.- 4. Complexity Theory.- II. 5. Building a Quantum Computer.- 6. Development Libraries for Quantum Computer Programming.- 7. Teleportation, Superdense Coding and Bell’s Inequality.- 8. The Canon: Code Walkthroughs.- 9. Quantum Computing Methods.- 10. Applications and Quantum Supremacy.- III. Toolkit.- 11. Mathematical Tools for Quantum Computing I.- 12. Mathematical Tools for Quantum Computing II.- 13. Mathematical Tools for Quantum Computing III.- 14. Dirac Notation.- 15. Table of Quantum Operators and Core Circuits.- Works Cited.- Index.

Read more less

Book SynopsisThis book introduces the fundamentals of the theory of quantum computing, illustrated with code samples written in Q#, a quantum-specific programming language, and its related Quantum Development Kit. Quantum computing (QC) is a multidisciplinary field that sits at the intersection of quantum physics, quantum information theory, computer science and mathematics, and which may revolutionize the world of computing and software engineering. The book begins by covering historical aspects of quantum theory and quantum computing, as well as offers a gentle, algebra-based, introduction to quantum mechanics, specifically focusing on concepts essential for the field of quantum programming. Quantum state description, state evolution, quantum measurement and the Bell’s theorem are among the topics covered. The readers also get a tour of the features of Q# and familiarize themselves with the QDK. Next, the core QC topics are discussed, complete with the necessary mathematical formalism. This includes the notions of qubit, quantum gates and quantum circuits. In addition to that, the book provides a detailed treatment of a series of important concepts from quantum information theory, in particular entanglement and the no-cloning theorem, followed by discussion about quantum key distribution and its various protocols. Finally, the canon of most important QC algorithms and algorithmic techniques is covered in-depth - from the Deutsch-Jozsa algorithm, through Grover’s search, to Quantum Fourier Transform, quantum phase estimation and Shor’s algorithm. The book is an accessible introduction into the vibrant and fascinating field of quantum computing, offering a blend of academic diligence with pragmatism that is so central to software development world. All of the discussed theoretical aspects of QC are accompanied by runnable code examples, providing the reader with two different angles - mathematical and programmatic - of looking at the same problem space. Table of ContentsPart One1 Background 1.1 Historical development of quantum theory 1.2 Reality without realism 2 Basics of quantum mechanics 2.1 Quantum state 2.2 Superposition 2.3 Born rule 2.4 Observables 2.5 State evolution 2.6 Larger systems 2.7 Postulates of quantum mechanics 2.8 Entanglement 2.9 Bell’s theorem 2.10 No-cloning theorem Part Two 3 Getting Started with Quantum Programming 3.1 Setting up QDK environment 3.2 Getting started with Q# 4 Quantum Computing 4.1 History 4.2 Qubits 4.3 Quantum circuits 4.4 Superposition 4.5 Pauli gates 4.5.1 I gate 4.5.2 X gate 4.5.3 Z gate 4.5.4 Y gate 4.5.5 Summary 4.6 Rotation gates 4.6.1 Rz gate 4.6.2 S gate 4.6.3 T gate 4.6.4 Rx and Ry gates 4.7 Multi qubit gates 4.7.1 Controlled gates 4.7.2 CNOT gate 4.7.3 SWAP gate 4.7.4 CZ gate 4.7.5 Toffoli gate 4.8 Gate universality 5 Entanglement 5.1 Basics 5.2 Bell’s inequalities 5.3 CHSH Game 5.4 Teleportation 5.5 Superdense coding 5.6 Entanglement as a resource 6 Quantum Key Distribution 6.1 One-time pad encryption 6.2 BB84 protocol 6.3 B92 protocol 6.4 EPR-based quantum key distribution Part Three 7 Algorithms 7.1 Deutsch-Jozsa Algorithm 7.2 QuantumSearch 7.3 Useful Algorithm Components 7.3.1 QFT 7.3.2 QPE 7.4 Shor’s Algorithm

Read more less

Book SynopsisThis book is to explore and explain the strategically sound capabilities at the synchronization between quantum computing and artificial intelligence (AI). The reader will be presented with an introduction and a deeper review of the technological trends and transitions being unearthed in the quantum computing and AI domains.

Read more less

Book SynopsisQuantum computers have demonstrated that they have the inherent potential to outperform classical computers in many areas. One of the major impacts is that the currently available cryptography algorithms are bound to no longer hold once quantum computers are able to compute at full speed. This book presents an overview of all the cross-disciplinary developments in cybersecurity that are being generated by the advancements in quantum computing.

Read more less

Book SynopsisQuantencomputing könnte die Informatik wie wir sie heute kennen revolutionieren. Die Möglichkeiten dieser Technologie sind enorm. Aber was steckt eigentlich dahinter? Mit diesem Buch führen Sie die Autoren so verständlich wie möglich in dieses komplexe Thema ein. Sie erklären Ihnen was es mit dem Quantencomputing überhaupt auf sich hat und erläutern die mathematischen und physikalischen Modelle, die ihm zugrunde liegen. Sie vergleichen Quantencomputing mit der aktuellen Informatik und werfen einen Blick darauf welche Anwendungen dadurch schon bald und welche in der weiteren Zukunft denkbar sind.Table of ContentsÜber den Autor 9 Einleitung 21 Über dieses Buch 21 Törichte Annahmen über die Leser 21 Vor welchen speziellen Herausforderungen standen wir? 23 Wo liegen die verstandesmäßigen Knackpunkte? 23 Damit stehen wir vor der folgenden Aufgabe 24 Umgang mit der Komplexität 24 Was muten wir zu? 25 Wie dieses Buch aufgebaut ist 26 Eingestreute »two cents« 28 Was wir draußen ließen 28 Konventionen und Symbole in diesem Buch 29 Danksagungen 29 Widmungen 30 Teil I: Neue Phänomene und neue Betrachtungsweisen 31 Kapitel 1 Quantencomputing – hope or hype? 35 Analogcomputer – Digitalcomputer – Quantencomputer 36 Konzepte des Quantencomputers 37 Verheißungen 38 Höher – schneller – weiter 38 Ein heiliger Gral des Quantencomputing 39 Verheißungen im Überblick 40 Berechenbarkeit und ihre Grenzen 41 Weitere Vereinheitlichungen in der Physik 41 Die Welt als prinzipiell berechenbares Uhrwerk 42 Neue Vorstellungen – neue Formeln – neue Datenstrukturen 42 Kapitel 2 Unterschiede, die einen Unterschied machen 47 Bits und Qubits 48 Bits 48 Qubits 48 Das geometrische Bild eines Qubit 49 Algebraische Beschreibung eines Qubit 53 Im Herzen des Quantencomputing 55 Ein erster Einstieg – dense coding 55 Operationen mit Vektoren – Ausblick auf Matrizen 59 Kapitel 3 Matrizen 61 Zum Einsatz und zur Handhabung von Matrizen 61 Beispiel: Fertigungskosten und ihre Abhängigkeiten 62 Zwischenbetrachtung: Klassische Bits und Bitfolgen als Vektoren 64 Bits implementiert als spezielle Qubits 64 Irritationen beim Übergang zum kartesischen Produkt 65 Wenn nicht das kartesische Produkt – was dann? 66 Welche Hypothek gehen wir mit dem Tensorprodukt gegenüber der Natur ein? 67 Bits als Vektoren: ein erstes Resümee 70 Bellzustände 71 Lineare Operationen auf Tensorräumen 71 Operationen zur Erzeugung einer Bell-Basis 71 Transformationen der Bell-Basis 75 Was ist nun das Besondere der Bell-Basis 77 Dense coding – revisited 79 Ausblicke 80 Kapitel 4 Teleportation – abstrakt und physikalisch 81 Beam me up, Scotty 82 Teleportation für Mathematiker 82 Ein erstes Resümee der mathematischen Beschreibung 87 Teleportation für Physiker 87 Resümee der physikalischen Beschreibung 94 Teil II: Neue Spielregeln in der Physik 95 Kapitel 5 Hinter dem Monitor 97 Die klassische Sichtweise 98 Klassische Physik 98 Ein Blick hinter den Monitor… 99 … und hinter die Physik 99 Kapitel 6 Abstieg in die Unterwelt 103 Geänderte Spielregeln 104 Skalierungen 104 »Law without law« 105 Berechnungen des Zufalls 106 Was läuft in der Mikrophysik »schief« – oder besser: anders 112 Auf welche Weise kommen Elementarereignisse und ihre Wahrscheinlichkeiten zustande? 112 Amplituden – Zusammenfassung ihrer funktionalen Prinzipien 120 R-Prozesse – Messungen 121 Doppelspalt – revisited 122 U-Prozesse – ungestörte Dynamik 125 Beschreibung der U-Prozesse 126 Einige »Gretchenfragen« 126 Infinite (?) Regresse 126 Management Summary 127 Der zu zahlende Preis 128 Letzte Notizen zum Messproblem in der Quantenmechanik 129 Versuche der Widerspruchsauflösung 130 Teil III: Qubits und ihre Operatoren 133 Kapitel 7 Bits – als Vektoren betrachtet 135 Bits und Qubits 136 Vorbereitung des Übergangs von Bits zu Qubits – Bits als Vektoren 136 Der Übergang von logischen Operationen zu unitären Operatoren – ternäre Operatoren 142 Wo stehen wir nun – und wo wollen wir hin? 146 Kapitel 8 Qubits – revisited 147 Qubits und ihre Operatoren 147 Das einzelne Qubit und seine Blochsphäre 148 Unitäre Operatoren auf dem einzelnen Qubit 152 Noch mehr unitäre Operatoren 157 Universalitätseigenschaften der Qubit-Operationen 162 Notizen zu physikalischen Implementierungen 163 Quantensysteme mit zwei (ausgezeichneten) Zuständen 164 Kapitel 9 Methoden der Fehlerbehandlung 165 Das No-Cloning-Theorem 166 Bitflip-Codes 167 Implementierung des Bitflip-Codes 167 Zur Messbarkeit einzelner Bitflips 168 Identifikation und Korrektur eines Bitflips an beliebiger Stelle 170 Phasenflip-Codes 171 Rückführung von Phasenflips auf Bitflips 172 Shor-Code 173 Teil IV: Quantenfouriertransformationen und mehr 175 Kapitel 10 Fouriertransformationen 177 Vorüberlegungen zur Fourieranalyse 178 Periodische Funktionen 178 Zur Fourieranalyse 180 Formeln der Fourieranalyse 181 Auf dem Weg zur diskreten Fouriertransformation 183 Ein kurzer Steilkurs in Modulorechnung 183 Die Relevanz der Ordnung einer Klasse für die Primfaktorzerlegung 185 Zwischenresümee: Wo stehen wir, wo wollen wir hin? 185 Eine Herleitung der diskreten Fouriertransformation 186 Übergang von einer Zahlenfolge zu einer Treppenfunktion 187 Die diskrete Fouriertransformation als lineare Abbildung 188 Normierung der Transformationsmatrix 189 Die Quantenfouriertransformation 190 Zur Power eines N-Qubit-Systems 190 Codierung der Basis eines N-Qubit-Systems 191 Eingaben in die Quantenfouriertransformation 192 Zur Aufbereitung der Quantenfouriertransformierten 193 Dualbrüche in e2πi kj 2n 194 Abschließende Regruppierung der Quantenfouriertransformierten 196 Management Summary: Mathematische Aufbereitung der Quantenfouriertransformierten 198 Implementierung der Quantenfouriertransformation 198 Gewinnung des Phasenfaktors e(2πi)(0,jn−l+1···jn)2 199 Schaltbilder für die Quantenfouriertransformation 201 Kapitel 11 Anwendungen der Quantenfouriertransformation 203 Phasenschätzung 204 Iterierte U-Operationen 204 Spezialfall: 𝜑 = (0, 𝜑1𝜑2 · · · 𝜑t)2 205 Näherungen 207 Management Summery: Phasenabschätzung von e2πi𝜑 210 Folgerungen der Phasenabschätzung: Wege zum Bestimmen der »Ordnung« einer Zahl 211 Iterierte Multiplikation mit einem festen [x] 211 Parallele Verarbeitung der Eigenvektoren |us⟩ 213 Finale der Berechnung der Ordnung 215 Management Summery: Berechnung der Ordnung einer Zahl 216 Der Shor-Agorithmus 217 Konsequenzen für die Kryptologie 218 Teil V: Weitere Anwendungen 219 Kapitel 12 »Feind hört (nicht) mit« 221 Zum Einstein-Podolski-Rosen-Paradoxon 221 Bellzustand zweier Teilchen mit Spin 221 Hidden variables 222 »second two cents« 222 Die bellsche Ungleichung 223 Berechnung der Erwartungswerte 224 Unvereinbarkeit der bellschen Ungleichung mit der Quantenmechanik 226 Rollentausch: Teilchen im Bellzustand als Münzen 226 Die Rechnungen im Einzelnen 228 Relevanz der bellschen Ungleichung für Verschlüsselungsverfahren 231 (K)ein »Knacken in der Leitung« 232 Symmetrische und asymmetrische Verfahren 233 Die Funktionsweise symmetrischer Verschlüsselungsverfahren 233 Das BB84-Protokoll 234 Zusammenfassung des BB84-Protokolls 239 E91-Protokoll 240 Kombination mit klassischen Verschlüsselungsverfahren 242 Kapitel 13 Wer suchet, der findet (schneller) 245 Die Suche im Heuhaufen 245 Benutzung eines Quantenschaltkreises 245 Idee des Grover-Algorithmus 246 Analyse der Grover-Iterationen 246 Kapitel 14 Zur Quantensimulation durch Quanten 251 Bemerkungen zu analogen Verfahren 252 Gradientenstrategien 252 Adiabatisches Quantencomputing 254 Zum adiabatischen Theorem der Quantenmechanik 255 Teil VI: Top Ten Teil 261 Kapitel 15 Ein Zusammenspiel von Physik, Mathematik, Informatik und Ingenieurwissenschaften in 10 Schritten 263 Und in fernerer Zukunft? – Vision in Rosa 266 Anhang 267 Anhang A Theoreme zur klassischen Zahlentheorie 269 Restklassenringe 269 Wohldefiniertheit der Operationen auf den Restklassen 270 Der euklidische Algorithmus 271 Einheiten in ℤn 272 Eulersche 𝜑-Funktion 272 Return on Invest – das RSA-Verfahren in der Kryptologie 273 Asymmetrische Verschlüsselungsverfahren 274 Das RSA-Verfahren in der Theorie 274 Praktische Bemerkungen zum RSA-Verfahren 276 Faktorisierung 277 Auffinden eines nichttrivialen Faktors von n 277 Notizen zu Kettenbrüchen 278 Kettenbrüche und ihre Konvergenten 279 Finale des Auffindens der gesuchten Ordnung r 281 Anhang B Komplexe Zahlen 283 Addition und Multiplikation 283 Definition der Multiplikation 284 Vektoren in der Rolle komplexer Zahlen 285 Wichtige Kenngrößen 285 Die komplexe e-Funktion 286 Komplexe Zahlen in Polarkoordinaten 287 Komplexe Zahlen als Matrizen 288 Anhang C Stochastik 291 Einführung 291 Ereignisse und Elementarereignisse 291 Wahrscheinlichkeiten 293 Wahrscheinlichkeitsräume 294 Benutzung mengentheoretischer Operationen 294 Bedingte Wahrscheinlichkeit und stochastische Unabängigkeit 295 Regeln zur Berechnung der Wahrscheinlichkeiten mengentheoretisch verknüpfter Ereignisse 295 Wahrscheinlichkeitsräume in der Quantenmechanik 297 Elementarereignisse in der Mikrowelt 297 Resümee 298 Anhang D Identische Teilchen 301 Klassischer Münzwurf 301 Analyse des Münzwurfs 303 »Münzwurf« mit Mikroteilchen 303 Anhang E Lineare Algebra in a nutshell 307 Vektoren 307 Addition 307 Skalare Multiplikation 309 Skalarprodukt 309 Darstellung von Vektoren im dreidimensionalen Raum 310 Abstrakte Vektorräume 311 Charakterisierung eines abstrakten Vektorraums 311 Besonderheiten des komplexen Skalarprodukts 312 Linearkombinationen, Basen und Dimensionen 312 Normierte Vektoren und Orthonormalbasen 313 Hilberträume 313 Kartesische und Tensorprodukte 314 Tensorprodukte 314 Lineare Abbildungen 315 Lineare Abbildungen und Matrizen 315 Eigenwerte und Eigenvektoren 316 Matrizen und Tensorprodukte 316 Skalarprodukte auf Tensorräumen 317 Unitäre Operatoren 317 Hermitesche Operatoren 317 Anhang F Wichtige Hermitesche Operatoren in der Quantenmechanik 319 Zur physikalischen Interpretation der Wellenfunktion 321 Repräsentation der Messapparate 322 Die Observablen für Ort und Impuls 324 Überblick über die Darstellungen des Orts- und Impulsoperators 327 Der Hamiltonoperator 330 Eigenwerte und Eigenfunktionen eines freien Teilchens 331 Anhang G Schrödingergleichung 333 Bedeutung von e−iH⋅t ℏ 333 Zur effizienten Berechenbarkeit der Lösungen 335 Letzte Spekulationen 336 Anhang H Symbolverzeichnis 339 Abbildungsverzeichnis 341 Stichwortverzeichnis 347

Read more less

Book SynopsisThis book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.Table of Contents1 Introduction 2 Classical Computer 2.1 Binary Representation 3 Quantum Computer 3.1 Qubit 4 Classical Gates and Circuits 5 Quantum Gates and Circuits 5.1 Hilbert space 5.2 Measurement 6 Deutsch Algorithm 7 Grover Algorithm 7.1 Grover algorithm: two-qubit 7.2 Grover algorithm: n-qubit 7.3 Grover diffusion and rotation gate G 7.4 Single Recursion: Two qubit 8 Deutsch-Josza Algorithm 9 Simon’s Algorithm 9.1 Quantum Algorithm 9.2 An Illustrative Example 10 Quantum Fourier Transform (QFT) 51 10.1 Quantum circuit of QFT 11 Shor 11.1 Introduction 11.2 Understanding the classical algorithm 11.3 Quantum algorithm 12 Option Pricing 12.1 Quantum Algorithm for Option Pricing 12.2 Quadratic Improvement 12.3 Estimation of Phase 12.4 Call Option 13 Solving Linear Equations 13.1 Introduction 13.2 Harrow-Hassidim-Lloyd Algorithm 13.3 Specific Example 13.4 Other applications 14 Quantum-Classical Hybrid Algorithms 14.1 Why bother? 14.2 Overlap of Wavefunctions 14.3 Variational Quantum Eigensolvers 15 Quantum Error Correction 15.1 Introduction 15.2 Simple quantum errors 15.3 Kraus Operators 15.4 Nine-qubit Code 15.5 General properties of quantum error-correcting codes 15.6 Classical Linear Codes 15.7 CSS Codes 16 Efficiency of a Quantum Computer 16.1 So where does quantum computation take place? 16.2 Conclusions 16.3 Acknowledgements

Read more less