Quantum Information and Quantum Computing : Proceedings of the Symposium.

By: Nakahara, MikioContributor(s): Sasaki, YoshitakaSeries: Kinki University Series on Quantum Computing SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2014Copyright date: ©2012Description: 1 online resource (194 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814425223Subject(s): Quantum computers -- Congresses.;Quantum theory -- Congresses.;Information theory -- CongressesGenre/Form: Electronic books. Additional physical formats: Print version:: Quantum Information and Quantum Computing : Proceedings of the SymposiumDDC classification: 004.14 LOC classification: QA76.889 -- .Q8486 2013ebOnline resources: Click to View
Contents:
Intro -- CONTENTS -- Preface -- Programme -- List of Participants -- 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 gates -- 4.2.2. 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. Ohmi -- 1. 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 system -- 3.2.2. 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. Sasaki -- 1. 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) -- Acknowledgements -- References -- Linear Preservers in Nonclassical Correlation Theories: An Introduction A. SaiToh, R. Rahimi and M. Nakahara -- 1. Introduction -- 2. Preserver Class EnCE -- 3. Example -- 4. Summary -- References -- Identification of the Hamiltonian of a 3-Particle Ising Model with Local Transverse Fields M. A. Fasihi, S. Tanaka, M. Nakahara and Y. Kondo -- 1. Introduction -- 2. Setup -- 3. Analysis -- 3.1. h1 = 0 case -- 3.2. Finite h1 case -- 3.3. |h1| » h2, h3, |J1|, |J2| case -- 3.4. Determination of signs of interactions -- 4. Conclusion -- Acknowledgments -- References.
How to Evaluate the Area Surrounded by Segments on a Unit Sphere? Y. Kondo -- 1. Introduction -- 2. Spherical Trigonometry -- 3. Quaternion -- 4. Parallel Transport and Geometric Phase -- 5. Area of Spherical Triangle -- 6. Pauli Matrices, Quantum State, and Quaternion -- 7. Quantum Mechanical Phases -- 8. Summary -- Acknowledgments -- References -- Microscopic Properties of Quantum Annealing-Application to Fully Frustrated Ising Systems S. Tanaka -- 1. Introduction -- 2. Computation Method -- 3. Quantum Fluctuation Effect of Frustrated Ising Systems -- 4. Conclusion -- References -- Implementation of Unitary Quantum Error Correction H. Tomita -- 1. Classical Error Correction (CEC) -- 2. Quantum Error Correction (QEC) -- 2.1. Quantum bit-flip error -- 2.2. Phase-flip error -- 2.3. The method of stabilizer -- 2.4. Collective error -- 3. Summary -- References -- Spin Crossover Properties of Iron(II) Complexes with a N4O2 Donor Set by Extended π-Conjugated Schiff-base Ligands T. Kuroda -- 1. Introduction -- 2. Experimental Section -- 2.1. Preparation of [Fe(qnal-21)2]CH2Cl2, (1) [7] -- 2.2. Preparation of [Fe(qnal-12)2]2C6H6 (2) -- 2.3. Preparation of powder sample of [Fe(Hqsalc)2] (3) -- 2.4. X-ray crystal structure determination -- 2.5. Magnetic susceptibility measurements -- 3. Results and discussion -- 3.1. Crystal structure of [Fe(qnal-21)2]CH2Cl2 (1) -- 3.2. Crystal structure of [Fe(qnal-12)2]2C6H6 (2) -- 3.3. Magnetic properties of 1 - 3 -- 3.4. Comparison of coordination geometries around Fe(II) ions in 1 and 2 -- 4. Conclusion -- 5. Acknowledgements -- References -- NMR Spectroscopic Studies of Light-Harvesting Bacteriochlorophylls Purified from Green Sulfur Photosynthetic Bacteria Y. Hirai and Y. Saga -- 1. Introduction -- 2. Materials and Methods -- 3. Results and Discussion -- References.
Spectroscopic Studies of Individual Extramembranous Light- Harvesting Complexes of Green Photosynthetic Bacteria Y. Saga -- 1. Introduction -- 2. Single Supramolecule Spectroscopy of Chlorosomes -- 3. Detection of Energy Transfer in Individual Chlorosomes -- 4. Summary -- References -- Entanglement Operator for a Multi-Qubit System C. Bagnasco, Y. Kondo and M. Nakahara -- 1. Introduction -- 2. Refocusing with "Hard" Pulses -- 3. Cancellation with Soft Pulse -- Acknowledgements -- References -- Some Topics in Coding Theory K. Chinen -- 1. What is coding theory? -- 2. Preliminaries -- 3. Zeta functions for linear codes -- 4. Recent results -- References.
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 working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of contributions will serve as a short introduction to these cutting edge research fields.
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Intro -- CONTENTS -- Preface -- Programme -- List of Participants -- 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 gates -- 4.2.2. 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. Ohmi -- 1. 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 system -- 3.2.2. 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. Sasaki -- 1. 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) -- Acknowledgements -- References -- Linear Preservers in Nonclassical Correlation Theories: An Introduction A. SaiToh, R. Rahimi and M. Nakahara -- 1. Introduction -- 2. Preserver Class EnCE -- 3. Example -- 4. Summary -- References -- Identification of the Hamiltonian of a 3-Particle Ising Model with Local Transverse Fields M. A. Fasihi, S. Tanaka, M. Nakahara and Y. Kondo -- 1. Introduction -- 2. Setup -- 3. Analysis -- 3.1. h1 = 0 case -- 3.2. Finite h1 case -- 3.3. |h1| » h2, h3, |J1|, |J2| case -- 3.4. Determination of signs of interactions -- 4. Conclusion -- Acknowledgments -- References.

How to Evaluate the Area Surrounded by Segments on a Unit Sphere? Y. Kondo -- 1. Introduction -- 2. Spherical Trigonometry -- 3. Quaternion -- 4. Parallel Transport and Geometric Phase -- 5. Area of Spherical Triangle -- 6. Pauli Matrices, Quantum State, and Quaternion -- 7. Quantum Mechanical Phases -- 8. Summary -- Acknowledgments -- References -- Microscopic Properties of Quantum Annealing-Application to Fully Frustrated Ising Systems S. Tanaka -- 1. Introduction -- 2. Computation Method -- 3. Quantum Fluctuation Effect of Frustrated Ising Systems -- 4. Conclusion -- References -- Implementation of Unitary Quantum Error Correction H. Tomita -- 1. Classical Error Correction (CEC) -- 2. Quantum Error Correction (QEC) -- 2.1. Quantum bit-flip error -- 2.2. Phase-flip error -- 2.3. The method of stabilizer -- 2.4. Collective error -- 3. Summary -- References -- Spin Crossover Properties of Iron(II) Complexes with a N4O2 Donor Set by Extended π-Conjugated Schiff-base Ligands T. Kuroda -- 1. Introduction -- 2. Experimental Section -- 2.1. Preparation of [Fe(qnal-21)2]CH2Cl2, (1) [7] -- 2.2. Preparation of [Fe(qnal-12)2]2C6H6 (2) -- 2.3. Preparation of powder sample of [Fe(Hqsalc)2] (3) -- 2.4. X-ray crystal structure determination -- 2.5. Magnetic susceptibility measurements -- 3. Results and discussion -- 3.1. Crystal structure of [Fe(qnal-21)2]CH2Cl2 (1) -- 3.2. Crystal structure of [Fe(qnal-12)2]2C6H6 (2) -- 3.3. Magnetic properties of 1 - 3 -- 3.4. Comparison of coordination geometries around Fe(II) ions in 1 and 2 -- 4. Conclusion -- 5. Acknowledgements -- References -- NMR Spectroscopic Studies of Light-Harvesting Bacteriochlorophylls Purified from Green Sulfur Photosynthetic Bacteria Y. Hirai and Y. Saga -- 1. Introduction -- 2. Materials and Methods -- 3. Results and Discussion -- References.

Spectroscopic Studies of Individual Extramembranous Light- Harvesting Complexes of Green Photosynthetic Bacteria Y. Saga -- 1. Introduction -- 2. Single Supramolecule Spectroscopy of Chlorosomes -- 3. Detection of Energy Transfer in Individual Chlorosomes -- 4. Summary -- References -- Entanglement Operator for a Multi-Qubit System C. Bagnasco, Y. Kondo and M. Nakahara -- 1. Introduction -- 2. Refocusing with "Hard" Pulses -- 3. Cancellation with Soft Pulse -- Acknowledgements -- References -- Some Topics in Coding Theory K. Chinen -- 1. What is coding theory? -- 2. Preliminaries -- 3. Zeta functions for linear codes -- 4. Recent results -- References.

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 working under this project. These contributions introduce NMR quantum computing and related techniques, number theory and coding theory, quantum error correction, photosynthesis, non-classical correlations and entanglement, neutral atom quantum computer, among others. Each of contributions will serve as a short introduction to these cutting edge research fields.

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