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Quantum Information and Computation

NMR quantum computing - lessons for the future

Lieven M. K. Vandersypen, Isaac L. Chuang

Published Dec 1, 2001• 2 citations
Publisher

Abstract

Future physical implementations of large-scale quantum computers will face significant practical challenges. Many useful lessons can be drawn from present results with Nuclear Magnetic Resonance realizations of controllable two, three, five, and seven qubit quantum systems. We summarize various experimental methods and theoretical procedures learned in this work which will be of considerable value in building and testing quantum processors with a wide variety of physical systems.

DOI
10.26421/qic1.s-15

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Future physical implementations of large-scale quantum computers will face significant practical challenges. Many useful lessons can be drawn from present results with Nuclear Magnetic Resonance realizations of controllable two, three, five, and seven qubit quantum systems. We summarize various experimental methods and theoretical procedures learned in this work which will be of considerable value in building and testing quantum processors with a wide variety of physical systems.
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Nuclear magnetic resonance (NMR) spectroscopy has proven to be a facile means of achieving small-scale demonstrations of quantum information processing. This was in large part made possible by the sophisticated methods of quantum control that have been developed by the NMR community over a span of more than 50 years. The traditional control methods, already perhaps the most complex examples of open-loop control available, were nevertheless designed primarily to assist in identifying the physical parameters of the underlying spin system, rather than to control the system with high precision. We have therefore extended the traditional methods in a variety of ways so as to achieve precise control, by taking advantage of prior knowledge of the physical parameters as determined by traditional methods. Due to the experimental challenges of real-time control, these developments relied upon our ability to simulate the evolution of the system under the action of radio-frequency control fields with essentially arbitrary precision, subject only to the available computing power. This talk presents an overview of our work in quantum control together with some of the on-going challenges still facing us
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.
Nuclear Magnetic Resonance (NMR) forms a natural test-bed to perform quantum information processing (QIP) and has so far proven to be one of the most successful quantum information processors. The nuclear spins in a molecule treated as quantum bits or qubits which are the basic building blocks of a quantum computer. The development of NMR over half a century puts it in a platform where we can utilize its excellent control techniques over an ensemble of spin systems and perform quantum computation in a highly controlled way. Apart from a successful quantum information processor, NMR is also a highly powerful quantum platform where many of the potentially challenging quantum mechanical experiments can be performed.
We have taken significant steps towards the realization of a practical quantum computer: using nuclear spins and magnetic resonance techniques at room temperature, we provided proof of principle of quantum computing in a series of experiments which culminated in the implementation of the simplest instance of Shor's quantum algorithm for prime factorization (15=3x5), using a seven-spin molecule. This algorithm achieves an exponential advantage over the best known classical factoring algorithms and its implementation represents a milestone in the experimental exploration of quantum computation. These remarkable successes have been made possible by the synthesis of suitable molecules and the development of many novel techniques for initialization, coherent control and readout of the state of multiple coupled nuclear spins. Furthermore, we devised and implemented a model to simulate both unitary and decoherence processes in these systems, in order to study and quantify the impact of various technological as well as fundamental sources of errors. In summary, this work has given us a much needed practical appreciation of what it takes to build a quantum computer. While liquid NMR quantum computing has well-understood scaling limitations, many of the techniques that originated from this research may find use in other, perhaps more scalable quantum computer implementations.
There has been much recent effort to realize quantum devices in many different physical systems. Among them, nuclear magnetic resonance (NMR) has been the first to demonstrate nontrivial quantum algorithms with small numbers of qubits and hence is a prototype for the key ingredients needed to build quantum computers. An important building block in many quantum applications is the scattering circuit, which can be used as a quantum multimeter to perform various quantum information processing tasks directly without recourse to quantum tomography. We implement in NMR a three-qubit version of the multimeter and also demonstrate a single-qubit fingerprinting.