# NMR Quantum Information Processing

**By**

- Ivan Oliveira, Centro Brasileiro De Pesquisas Fisicas, Rio De Janeiro, Brazil
- Roberto Sarthour Jr., Centro Brasileiro De Pesquisas Fisicas, Rio de Janeiro, Brazil
- Tito Bonagamba, Sao Paulo State University At Sao Carlos, Physics and Computing Science Department Sao Paulo, Brazil
- Eduardo Azevedo, Sao Paulo State University at Sao Carlos, Physics and Computing Science Department, Sao Paulo, Brazil
- Jair C. C. Freitas, Federal Universitty of Espirito Santo, Brazil

Quantum Computation and Quantum Information (QIP) deals with the identification and use of quantum resources for information processing. This includes three main branches of investigation: quantum algorithm design, quantum simulation andquantum communication, including quantum cryptography. Along the past few years, QIP has become one of the most active area ofresearch in both, theoretical and experimental physics, attracting students and researchers fascinated, not only by the potentialpractical applications of quantum computers, but also by the possibility of studying fundamental physics at the deepest level of quantum phenomena.**NMR Quantum Computation and Quantum Information Processing** describes the fundamentals of NMR QIP, and the main developments which can lead to a large-scale quantum processor.

The text starts with a general chapter onthe interesting topic of the physics of computation. The very first ideas which sparkled the development of QIP came from basic considerations of the physical processes underlying computational actions. In Chapter 2 it is made an introduction to NMR, including the hardware and other experimental aspects of the technique. InChapter 3 we revise the fundamentals of Quantum Computation and Quantum Information. The chapter is very much based on the extraordinary book of Michael A. Nielsen and Isaac L. Chuang, withan upgrade containing some of the latest developments, such as QIP in phase space, and telecloning. Chapter 4 describes how NMRgenerates quantum logic gates from radiofrequency pulses, upon which quantum protocols are built. It also describes the important technique of Quantum State Tomography for both, quadrupole and spin1/2 nuclei. Chapter 5 describes some of the main experiments of quantum algorithm implementation by NMR, quantum simulation and QIP in phase space. The important issue of entanglement in NMR QIPexperiments is discussed in Chapter 6. This has been a particularly exciting topic in the literature. The chapter contains a discussionon the theoretical aspects of NMR entanglement, as well as some of the main experiments where this phenomenon is reported. Finally, Chapter 7 is an attempt to address the future of NMR QIP, based invery recent developments in nanofabrication and single-spin detection experiments. Each chapter is followed by a number of problems and solutions.

View full description### Audience

For senior undergraduate students and graduates. It can also be used as a reference book inadvanced quantum mechanics courses and will be useful as a reference for research in the area of QIP, andother correlated areas.

### Book information

- Published: May 2007
- Imprint: ELSEVIER
- ISBN: 978-0-444-52782-0

### Table of Contents

**1. Physics, Information and Computation**1.1 Turing machines, logic gates and computers

1.2 Knowledge, statistics and thermodynamics

1.3 Reversible versus irreversible computation

1.4 Landauer's Principle and the Maxwell demon

1.5 Natural phenomena as computing processes: the physical limits of computation

1.6 The Moore's law: quantum computation**2. Nuclear Magnetic Resonance: Basics **2.1 General principles

2.2 Interaction with static magnetic fields

2.3 Interaction with a radiofrequency field - the resonance phenomenon

2.4 Relaxation phenomena

2.5 Density matrix formalism: populations, coherences, and NMR observables

2.6 NMR of non-interacting spins ½

2.7 Nuclear spin interactions

2.8 NMR of two coupled spins ½

2.9 NMR of quadrupolar nuclei

2.10 Density matrix approach to nuclear spin relaxation

2.11 Solid-state NMR

2.12 The experimental setup

2.13 Applications of NMR in science and technology **3. Fundamentals of Quantum Computation and Quantum Information**3.1 Historical development

3.2 The postulates of quantum mechanics

3.3 Classical and quantum bits

3.4 The computational basis and quantum logic gates

3.5 Quantum circuits

3.6 Quantum state tomography

3.7 Entanglement and its applications

3.8 Quantum algorithms

3.9 Quantum simulations

3.10 Quantum information in phase space

3.11 Telecloning **4. Introduction to NMR Quantum Computing**4.1 The NMR qubits

4.2 Quantum logic gates generated by radiofrequency pulses

4.3 Production of pseudo-pure states

4.4 Reconstruction of density matrices in NMR quantum computing: Quantum State Tomography

4.5 Monitoring quantum logic operations by Quantum State Tomography

4.6 Evolution of Bloch vectors and other quantities obtained by tomographed density matrices

4.7 The relaxation problem and source of errors in NMR-QC**5. Implementation of Quantum Algorithms by NMR**5.1 Numerical simulation of NMR spectra and density matrix calculation along an algorithm implementation

5.2 NMR implementation of Deutsch and Deutsch-Josza algorithms

5.3 Grover search tested by NMR

5.4 Quantum Fourier transform NMR implementation

5.5 Shor's factorization algorithm tested in a 7-qubit molecule

5.6 Algorithm implementation in quadrupole systems

5.7 NMR quantum simulation **6. Entanglement in Liquid-State NMR**6.1 The problem of liquid-state NMR entanglement

6.2 The Peres criterium and bounds for NMR entanglement

6.3 NMR experiments reporting entanglement **7. Perspectives for NMR Quantum Computation and Quantum Information**7.1 Silicon-based proposals: solution for the scaling problem

7.2 NMR quantum information processing based in Magnetic Resonance Force Microscopy

7.3 Single spin detection techniques: solution for the sensitivity problem

7.4 NMR on a chip: towards the NMR quantum chip integration.