Mathematical aspects of quantum computing 2007 / editors, Mikio Nakahara, Robabeh Rahimi, Akira SaiToh.

Format:

Book

Conference/Event

Contributor:

Nakahara, Mikio.

Rahimi, Robabeh.

SaiToh, Akira.

Kinki Daigaku.

Conference Name:

Mathematical Aspects of Quantum Computing (2007 : Osaka, Japan)

Series:

Kinki University series on quantum computing ; v. 1.

Kinki University series on quantum computing, 1793-7299 ; v. 1

Language:

English

Subjects (All):

Quantum computers--Congresses.

Quantum computers.

Quantum computers--Mathematics--Congresses.

Physical Description:

1 online resource (240 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, NJ : World Scientific, c2008.

Language Note:

English

Summary:

This book provides a comprehensive overview of the mathematical aspects of quantum computing. It will be useful for graduate students and researchers interested in quantum computing from different areas of physics, mathematics, informatics and computer science. The lecture notes in this volume are written in a self-contained style, and hence are accessible for graduate students and researchers with even less background in the topics. <i>Sample Chapter(s)</i><br>Quantum Computing: An Overview (804 KB)<br> <br><i>Contents:</i><ul><li>Quantum Computing: An Overview <i>(M Nakahara)</i></li><li>B

Contents:

CONTENTS; Preface; LIST OF PARTICIPANTS; Quantum Computing: An Overview M. Nakahara; 1. Introduction; 2. Quantum Physics; 2.1. Notation and conventions; 2.2. Axioms of quantum mechanics; 2.3. Simple example; 2.4. Multipartite system, tensor product and entangled state; 2.5. Mixed states and density matrices; 2.6. Negativity; 2.7. Partial trace and purification; 3. Qubits; 3.1. One qubit; 3.2. Bloch sphere; 3.3. Multi-qubit systems and entangled states; 4. Quantum Gates, Quantum Circuit and Quantum Computation; 4.1. Introduction; 4.2. Quantum gates; 4.2.1. Simple quantum gates

4.2.2. Walsh-Hadamard transformation 4.2.3. SWAP gate and Fredkin gate; 4.3. No-cloning theorem; 4.4. Quantum teleportation; 4.5. Universal quantum gates; 4.6. Quantum parallelism and entanglement; 5. Simple Quantum Algorithms; 5.1. Deutsch algorithm; 5.2. Deutsch-Jozsa algorithm; 6. Decoherence; 6.1. Open quantum system; 6.1.1. Quantum operations and Kraus operators; 6.1.2. Operator-sum representation and noisy quantum channel; 6.1.3. Completely positive maps; 6.2. Measurements as quantum operations; 6.2.1. Projective measurements; 6.2.2. POVM; 6.3. Examples; 6.3.1. Bit- flip channel

6.3.2. Phase-flip channel 7. Quantum Error Correcting Codes; 7.1. Introduction; 7.2. Three-qubit bit-flip code: the simplest example; 7.2.1. Bit-flip QECC; 7.2.2. Encoding; 7.2.3. Transmission; 7.2.4. Error syndrome dectection and correction; 7.2.5. Decoding; 7.2.6. Miracle of entanglement; 7.2.7. Continuous rotations; 8. DiVincenzo Criteria; 8.1. DiVincenzo criteria; 8.2. Physical realizations; Acknowledgements; References; Braid Group and Topological Quantum Computing T. Ootsuka, K. Sakuma; 1. Introduction; 2. Braid Groups; 3. Knots Defined by Braids; 4. Topological Quantum Computing

5. Anyon Model6. Fibonacci Anyons; Appendix A. Fundamental group; References; An Introduction to Entanglement Theory D. J. H. Markham; 1. Introduction; 2. Quantum Mechanics and State Space; 2.1. State space; 2.2. Evolution; 2.3. POVMs, projective measurement and observables; 2.4. Composite systems; 3. Entanglement and Separability; 4. Quantification of Entanglement; 4.1. Local operations and classical communication; 4.2. Entanglement measures; 4.3. Uniqueness of measures, order on states; 4.4. Measuring entanglement; 4.5. Multipartite entanglement; 5. Conclusions; References

Holonomic Quantum Computing and Its Optimization S. Tanimura1. Introduction; 2. Holonomies in Mathematics and Physics; 2.1. Holonomy in Riemannian geometry; 2.2. Berry phase in quantum mechanics; 2.3. Wilczek-Zee holonomy in quantum mechanics; 2.4. Examples; 2.4.1. Berry phase; 2.4.2. Λ-type system; 3. Holonomic Quantum Computer; 4. Formulation of the Problem and its Solution; 4.1. Geometrical setting; 4.2. The isoholonomic problem; 4.3. The solution: horizontal extremal curve; 5. The Boundary-Value Problem; 5.1. Equivalence class; 5.2. U(1) holonomy; 5.3. U(k) holonomy

6. Examples of Unitary Gates

Notes:

"This volume contains lecture notes and poster contributions presented at the summer school "Mathematical Aspects of Quantum Computing", held from 27 to 29 August, 2007 at Kinki University in Osaka, Japan"--P. [v].

Includes bibliographical references.

ISBN:

9786611968137

9781281968135

1281968137

9789812814487

9812814485

OCLC:

879023424