NMR QUANTUM INFORMATION PROCESSING
CONTENTS BRIEF HISTORICAL SURVEY AND PERSPECTIVES REFERENCES PHYSICS, INFORMATION AND COMPUTATION TURING MACHINES, LOGIC GATES AND COMPUTERS KNOWLEDGE, STATISTICS AND THERMODYNAMICS REVERSIBLE VERSUS IRREVERSIBLE COMPUTATION LANDAUER’S PRINCIPLE AND THE MAXWELL DEMON NATURAL PHENOMENA AS COMPUTING PROCESSES THE PHYSICAL LIMITS OF COMPUTATION MOORE’S LAW QUANTUM COMPUTATION PROBLEMS WITH SOLUTIONS BASIC CONCEPTS ON NUCLEAR MAGNETIC RESONANCE GENERAL PRINCIPLES INTERACTION WITH STATIC MAGNETIC ?ELDS INTERACTION WITH A RADIOFREQUENCY ?ELD – THE RESONANCE PHENOMENON RELAXATION PHENOMENA DENSITY MATRIX FORMALISM: POPULATIONS, COHERENCES, AND NMR OBSERVABLES NMR OF NON-INTERACTING SPINS 1/2 NUCLEAR SPIN INTERACTIONS CHEMICAL SHIFT DIPOLAR COUPLING J -COUPLING QUADRUPOLAR COUPLING GENERAL FORM OF THE INTERNAL HAMILTONIANS NMR OF QUADRUPOLAR NUCLEI 210 DENSITY MATRIX APPROACH TO NUCLEAR SPIN RELAXATION 211 SOLID-STATE NMR DIPOLAR DECOUPLING MAGIC-ANGLE SPINNING (MAS) CROSS-POLARIZATION (CP) THE CP-MAS EXPERIMENT 212 THE EXPERIMENTAL SETUP 213 APPLICATIONS OF NMR IN SCIENCE AND TECHNOLOGY FUNDAMENTALS OF QUANTUM COMPUTATION AND QUANTUM INFORMATION HISTORICAL DEVELOPMENT THE POSTULATES OF QUANTUM MECHANICS QUANTUM BITS QUANTUM LOGIC GATES SOME EXAMPLES OF APPLICATION OF THE POSTULATES THE CONTROLLED NOT – CNOT – GATE GRAPHICAL REPRESENTATION OF GATES AND QUANTUM CIRCUITS THE SWAP LOGIC GATE THE QUANTUM FOURIER TRANSFORM – QFT QUANTUM STATE TOMOGRAPHY THE DENSITY MATRIX DETERMINING ? ENTANGLEMENT SOME APPLICATIONS OF ENTANGLEMENT QUANTUM ALGORITHMS THE DEUTSCH’S ALGORITHM THE QUANTUM SEARCH ALGORITHM THE QUANTUM FACTORIZING ALGORITHM QUANTUM SIMULATIONS 310 QUANTUM INFORMATION IN PHASE SPACE 3101 THE WIGNER FUNCTION 3102 MEASURING THE WIGNER FUNCTION 3103 QUANTUM STATES IN PHASE SPACE 311 DETERMINING EIGENVALUES AND EIGENVECTORS INTRODUCTION TO NMR QUANTUM COMPUTING THE NMR QUBITS QUANTUM LOGIC GATES GENERATED BY RADIOFREQUENCY PULSES ELEMENTARY SINGLE-QUBIT GATES AND THEIR IMPLEMENTATIONS USING RF PULSES ELEMENTARY TWO-QUBIT GATES AND THEIR IMPLEMENTATION IN NMR MULTI-QUBIT GATES USE OF STRONGLY MODULATED RF PULSES FOR QUANTUM GATE IMPLEMENTATION IN NMR QIP PRODUCTION OF PSEUDO-PURE STATES TEMPORAL AVERAGING SPATIAL AVERAGING STATE LABELING RECONSTRUCTION OF DENSITY MATRICES IN NMR QIP: QUANTUM STATE TOMOGRAPHY NMR QUANTUM STATE TOMOGRAPHY NMR QUANTUM STATE TOMOGRAPHY IN COUPLED SPIN 1/2 SYSTEMS NMR QUANTUM STATE TOMOGRAPHY OF QUADRUPOLE NUCLEI EVOLUTION OF BLOCH VECTORS AND OTHER QUANTITIES OBTAINED FROM TOMOGRAPHED DENSITY MATRICES IMPLEMENTATION OF QUANTUM ALGORITHMS BY NMR NUMERICAL SIMULATION OF NMR SPECTRA AND DENSITY MATRIX CALCULATION ALONG AN ALGORITHM IMPLEMENTATION NMR IMPLEMENTATION OF DEUTSCH AND DEUTSCH–JOZSA ALGORITHMS GROVER SEARCH TESTED BY NMR QUANTUM FOURIER TRANSFORM NMR IMPLEMENTATION SHOR FACTORIZATION ALGORITHM TESTED IN A 7-QUBIT MOLECULE ALGORITHM IMPLEMENTATION IN QUADRUPOLE SYSTEMS MEASURING THE DISCRETE WIGNER FUNCTION ENTANGLEMENT IN LIQUID-STATE NMR THE PROBLEM OF LIQUID-STATE NMR ENTANGLEMENT THE PERES CRITERIUM AND BOUNDS FOR NMR ENTANGLEMENT SOME NMR EXPERIMENTS REPORTING PSEUDO-ENTANGLEMENT