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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Preface

Ivan S. Oliveira, Roberto M. Serra

Published Sep 3, 2012• 2 citations
Publisher

Abstract

Pulsed nuclear magnetic resonance (NMR) was discovered in 1950 by Erwin L. Hahn.In 62 years of use, the technique has definitely been established as one of the main tools of investigation in physics, chemistry, biology and medicine.Since 1950, NMR has yielded four Nobel Prizes: one in physics (F.Bloch and E. M. Purcell, in 1952), two in chemistry (R. R. Ernst, in 1991 and K. Wüthrich, in 2002) and one in medicine (P.C. Lauterbur and P. M. Mansfield, in 2003).Before the 'pulsed-era', Otto Stern and Isidor Rabi also won the Prize with NMR, in 1943 and 1944, respectively.From the year 1997, pulsed NMR met a novel and exciting area of investigation: quantum information processing (QIP).Nuclear spins are qubits, and radiofrequency pulses are unitary transformations.Add to this some nonunitary operations, such as averages, and voila: spin thermal states in samples at room temperature can behave like pure quantum states, allowing complete quantum algorithms and protocols to be implemented in small molecular quantum computers.For the past 15 years, over 500 papers have appeared in the literature of NMR-QIP and has led to a huge amount of original results, in essentially every single area of research within quantum information and quantum computation: quantum algorithm implementation, quantum communication protocols, simulation of quantum systems (optical systems, condensed matter, Bose-Einstein condensates, harmonic oscillators, etc.), quantum error correction codes, tests of Bell-like inequality violations, tools to characterize and quantify entanglement, studies of decoherence of quantum states in open systems and so on.New NMR tools have been developed, such as strong modulating pulse and gradient ascent pulse engineering techniques for radiofrequency pulse engineering, and sophisticated experiments have been published using these techniques.No other quantum information technique has contributed so much to the area.Such a stimulating activity has resulted in the proposal of the present issue, which gathers many of the experts in the field of NMR-QIP around the world.It has contributions from groups from 10 countries: Argentina, Brazil, Canada, China, UK, Germany, Japan, Russia, Singapore and USA.They describe the state-of-the-art of NMR-QIP, adding various novelties to it.During the organization, it has been a most rewarding experience to interact with these colleagues, and we thank them all for their participation in the project.We are sure that this issue will greatly increase cooperation among groups, and encourage students to enter this promising area, resulting in a healthy feedback to NMR-QIP development.

DOI
10.1098/rsta.2012.0333

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Pulsed nuclear magnetic resonance (NMR) was discovered in 1950 by Erwin L. Hahn.In 62 years of use, the technique has definitely been established as one of the main tools of investigation in physics, chemistry, biology and medicine.Since 1950, NMR has yielded four Nobel Prizes: one in physics (F.Bloch and E. M. Purcell, in 1952), two in chemistry (R. R. Ernst, in 1991 and K. Wüthrich, in 2002) and one in medicine (P.C. Lauterbur and P. M. Mansfield, in 2003).Before the 'pulsed-era', Otto Stern and Isidor Rabi also won the Prize with NMR, in 1943 and 1944, respectively.From the year 1997, pulsed NMR met a novel and exciting area of investigation: quantum information processing (QIP).Nuclear spins are qubits, and radiofrequency pulses are unitary transformations.Add to this some nonunitary operations, such as averages, and voila: spin thermal states in samples at room temperature can behave like pure quantum states, allowing complete quantum algorithms and protocols to be implemented in small molecular quantum computers.For the past 15 years, over 500 papers have appeared in the literature of NMR-QIP and has led to a huge amount of original results, in essentially every single area of research within quantum information and quantum computation: quantum algorithm implementation, quantum communication protocols, simulation of quantum systems (optical systems, condensed matter, Bose-Einstein condensates, harmonic oscillators, etc.), quantum error correction codes, tests of Bell-like inequality violations, tools to characterize and quantify entanglement, studies of decoherence of quantum states in open systems and so on.New NMR tools have been developed, such as strong modulating pulse and gradient ascent pulse engineering techniques for radiofrequency pulse engineering, and sophisticated experiments have been published using these techniques.No other quantum information technique has contributed so much to the area.Such a stimulating activity has resulted in the proposal of the present issue, which gathers many of the experts in the field of NMR-QIP around the world.It has contributions from groups from 10 countries: Argentina, Brazil, Canada, China, UK, Germany, Japan, Russia, Singapore and USA.They describe the state-of-the-art of NMR-QIP, adding various novelties to it.During the organization, it has been a most rewarding experience to interact with these colleagues, and we thank them all for their participation in the project.We are sure that this issue will greatly increase cooperation among groups, and encourage students to enter this promising area, resulting in a healthy feedback to NMR-QIP development.
Regarding the end of the 1900s, a small community of researchers in physics, computer science, mathematics and chemistry began to explore the fertile ground at the intersection of quantum mechanics with information theory, which led to a new and powerful paradigm of quantum computing.Quantum information processing promises to extend today's computing resources.Quantum computers, theoretically, could solve problems much more quickly than any classic computer.Intensive experimental efforts have been made to implement quantum computing since Shor and Grover developed their algorithms.In 1997, Nuclear Magnetic Resonance (NMR) emerged as one of the most promising experimental techniques for the implementation of quantum computing protocols.The isolation of nuclear spins and consequent long relaxation times, combined with the perfect dynamics implemented by radiofrequency pulses, led to important studies in the area.Therefore, nuclear spins are picked out as good candidates for quantum bits.In this scenario, quantum chemistry covers a vast field of quantum information science and can lead to advances in scientific research.
After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this high degree of randomness, it is possible to investigate QIP because the relaxation time (the time scale over which useful signal from a computation is lost) is sufficiently long. We explain how this feature leads to the crucial ability of simulating a pure (non-random) state by using ``pseudopure'' states. We discuss how the ``answer'' provided by a computation is obtained by measurement and how this measurement differs from the ideal, projective measurement of QIP. We then give implementations of some simple quantum algorithms with a typical experimental result. We conclude with a discussion of what we have learned from NMR QIP so far and what the prospects for future NMR QIP experiments are.
Fifty years of developments in nuclear magnetic resonance (NMR) have resulted in an unrivaled degree of control of the dynamics of coupled two-level quantum systems. This coherent control of nuclear spin dynamics has recently been taken to a new level, motivated by the interest in quantum information processing. NMR has been the workhorse for the experimental implementation of quantum protocols, allowing exquisite control of systems up to seven qubits in size. This article surveys and summarizes a broad variety of pulse control and tomographic techniques which have been developed for, and used in, NMR quantum computation. Many of these will be useful in other quantum systems now being considered for the implementation of quantum information processing tasks.
In the last 20 years, there have been lots of novel developments and remarkable achievements in quantum information processing theoretically and experimentally. Among them, the coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance (NMR) system, especially in liquid-state NMR. Compared with other quantum information processing systems, NMR platform has many advantages such as the long coherence time, the precise manipulation and well-developed quantum control techniques, which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing and quantum simulation have been thoroughly studied over half a century. There are also many outstanding researches in the recent several years. So we focus on the recent researches in this review article. First, we introduce the basic principle of the liquid-state NMR quantum computing and two new methods reported in the pseudo-pure state preparation which has more advantages than the traditional methods. The quantum noise-injection methods and the quantum tomography technology in liquid-state NMR are also mentioned. Then we overview Horrow-Hassidim-Lioyd algorithm, quantum support vector machine algorithm, duality quantum computing and their implementations in liquid-state NMR system. Also, we report recent researches about quantum simulations, including quantum tunneling, high-energy physics and topological sequences. Then we display the quantum cloud platform of our group. In order to let more people, either amateurs or professionals, embrace and more importantly participate in the tidal wave of quantum science, we launch our NMR quantum cloud computing (NMRCloudQ) service. Through NMRCloudQ, we offer a direct access to a real, physical spectrometer in our laboratory and encourage users to explore quantum phenomena and demonstrate quantum algorithms. Finally, we discuss the development prospects and development bottlenecks of NMR, and point out the prospects for the future development direction.