Quantum information processing via nuclear magnetic resonance

Abstract

Our group has devoted efforts for the development of Quantum Computation and Quantum Information (QCQI) via NMR and has published articles and a book on the subject. We are currently intensifying collaborations in order to apply the developed methodologies for performing NMR experiments associated with more fundamental QCQI issues. For the development of new opportunities that are arising for our group, we need to acquire a 9.4 T superconducting magnet, since we already have NMR consoles able to perform advanced QCQI NMR experiments. As we do not have this magnet, we are unable to keep designing new experiments in our research Group, source of almost all experimental developments in this NMR research area in Brazil. This magnet had been requested within a project approved by FAPESP, however, due to the initial referee´s comments, we removed it from the proposal in order to accelerate its approval. However, we inserted detailed justifications for its acquisition. Although two of the new referee´s reviews indicated that the project should be approved in full, including the magnet, it was not included among the approved items. In terms of projects to be developed, we believe it is possible to implement a similar macroscopic of a quantum information processor by NMR. From the creation of pseudo-pure states, several protocols and quantum algorithms for quantum information processing (QIP) were implemented in such a system. NMR also allowed the experimental testing of various proposals related to QIP, with a precision rarely matched by other experimental techniques. Therefore, NMR is a powerful tool for testing the physical principles related to QIP. Specifically, for the states used as basis for the implementation of quantum protocols in NMR, known as pseudo-pure states, entanglement is not present, except in special experimental situations. This leads to questions about the quantum nature of NMR implementations for QIP. On the other hand, it was demonstrated that the presence of entangled states is a necessary but not sufficient to CQIQ. Also, NMR offers other important characteristics such as the handling and effectiveness of the implementation of quantum states. Considering that a key feature of NMR is the excellent control of the processing unitary transformations provided by the use of radio frequency pulses, it is seen that this technique provides unique methods, very effective for the QIP. Furthermore, we demonstrated that the existence of quantum correlations, different from entanglement, can be another reason for the success of the implementations by NMR. It is possible to measure such quantum correlations from a quantity called quantum discord. For some separable mixed states, or non-entangled states, quantum discord exhibits non-zero values, indicating the presence of nonclassical correlations more general than the entanglement. The algorithms that use these quantum correlations present advantages for QIP when compared to their classical analogues. Therefore, such a correlation appears to play a significant role in the protocols for processing of information. With this in mind, and also that the NMR states are separable mixed-states, we recently demonstrated theoretical-experimentally, via quantum state tomography and calculations of quantum discord, the existence of such correlations in a NMR system as well as the effects of decoherence on them. This study supports the idea that there is indeed a quantum nature of NMR implementations for PIQ. Among the most important projects we intend to develop with the use of the new superconducting magnet, taking into account the above considerations, we highlight: i) Measurements of classical and quantum correlations and their use in information processing by NMR, ii) studies of decoherence and quantum states protection using NMR iii) Geometric Phases and NMR, and iv) Simulation of quantum systems via bosonic NMR quadrupolar systems. (AU)