Quantum information and quantum computing / editors, Mikio Nakahara, Yoshitaka Sasaki.

Format:

Book

Conference/Event

Contributor:

Nakahara, Mikio.

Sasaki, Yoshitaka.

Conference Name:

Symposium on Quantum Information and Quantum Computing (2011 : Kinki University, Japan)

Symposium on Quantum Information and Quantum Computing (2011 : Osaka, Japan)

Series:

Kinki University series on quantum computing ; v. 6.

Kinki University series on quantum computing ; vol. 6

Language:

English

Subjects (All):

Quantum computers--Congresses.

Quantum computers.

Quantum theory--Congresses.

Quantum theory.

Information theory--Congresses.

Information theory.

Physical Description:

1 online resource (194 p.)

Edition:

1st ed.

Place of Publication:

Singapore : World Scientific, c2013.

Language Note:

English

Summary:

The open research center project "Interdisciplinary fundamental research toward realization of a quantum computer" has been supported by the Ministry of Education, Japan for five years. This is a collection of the research outcomes by the members engaged in the project. To make the presentation self-contained, it starts with an overview by Mikio Nakahara, which serves as a concise introduction to quantum information and quantum computing. Subsequent contributions include subjects from physics, chemistry, mathematics, and information science, reflecting upon the wide variety of scientists worki

Contents:

Preface; Programme; List of Participants; CONTENTS; Computing with Quanta M. Nakahara; 1. Introduction; 2. Quantum Physics; 2.1. Axioms of quantum mechanics; 2.2. Multipartite system; 2.3. Mixed states and density matrices; 2.4. Negativity; 2.5. Partial trace and purification; 2.6. von Neumann entropy; 2.6.1. Shannon entropy; 2.6.2. von Neumann entropy; 2.7. Nonclassical correlation other than entanglement; 3. Qubits; 3.1. One qubit; 3.2. Bloch sphere; 3.3. Multi-qubit systems; 4. Quantum Gates, Quantum Circuit and Quantum Computation; 4.1. Introduction; 4.2. Quantum gates

4.2.1. Simple quantum gates4.2.2. Walsh-Hadamard Transformation; 4.3. n-qubit gates; 4.4. Universality; 4.5. Quantum parallelism and entanglement; 5. Deutsch 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. Examples; 6.2.1. Bit-flip channel; 6.2.2. Phase-flip channel; 6.3. Quantum error correcting codes; 7. DiVincenzo Criteria; 7.1. DiVincenzo criteria; 7.2. Physical realizations; 8. Summary; Acknowledgements; References

Implementation of a Selective Two-Qubit Gate Operation in a Neutral Atom Quantum Computer E. H. Lapasar, K. Kasamatsu, Y. Kondo, M. Nakahara and T. Ohmi1. Introduction; 2. Analysis of the Two-qubit Gate Operation; 3. Execution Time and Fidelity; 4. Summary; Acknowledgements; References; Magnetic Resonance as an Experimental Device for Quantum Computing Research M. Chiba and Y. Kondo; 1. Introduction; 2. Low-field NMR for quantum computing; 3. NMR under Earth's field; 3.1. Experimental procedure of NMR under Earth's field; 3.2. Signal intensity of low-field NMR

3.2.1. Polarization of the proton spin system3.2.2. Magnetization of the proton spin system; 3.2.3. FID signal intensity; 3.3. Estimation of signal intensity of Earth's field NMR; 3.4. Estimation of signal to noise ratio; 3.5. Passage effect by turning off the poralization field; 4. Experimental result of Earth's field NMR; 4.1. FID signal and Fourier spectrum; 4.2. Homogeneity of the magnetic field; 5. Conclusion; Acknowledgements; References; Introduction to Surface Code Quantum Computation Y. Wan; 1. Overview; 2. Surface Code Quantum Computation; References

Quantum Computing and Number Theory Y. Sasaki1. Introduction; 2. Modular Arithmetic; 3. Period; 4. Miller's Algorithm; 4.1. Miller's Algorithm; 4.2. Example; 5. Shor's Period Finding Algorithm; 5.1. Period Finding Algorithm; 5.2. Remarks; 1.5.2.1. The orthogonal property of exponential sum; 5.2.2. The probability that two numbers are coprime; 6. Prime Number Theory; 6.1. Prime Number Theorem; 6.1.1. A brief sketch of the proof; 6.1.2. Remarks; 6.1.3. Unnecessary observation; 6.2. The Riemann Zeta-Function; 6.2.1. Special values of ζ(s) at positive integers

6.2.2. The infinite product expansion of (s)

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

1-283-73944-5

981-4425-22-2

OCLC:

818848245