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[The NMR implementation of quantum algorithm].

Xuemei Luo

Published Feb 1, 2003• 0 citations
OpenAlex

Abstract

A quantum computer is a device that processes information in a quantum-mechanically coherent fashion. In principle, it can exploit coherent quantum interference and entanglement to perform computations, such as factoring large numbers or searching an unsorted database, more rapidly than classical computers. Noise, decoherence, and manufacturing problems make constructing large scale quantum computers difficult. Ion traps and optical cavities offer promising experimental approaches, but no quantum algorithm has yet been implemented with those systems. On the other hand, because of their natural isolation from the environment, nuclear spins are particularly good 'quantum bits', and their use for quantum computation is possible by applying nuclear magnetic resonance (NMR) techniques in an unconventional manner. Here, we report on the experimental implementation of a quantum algorithm using NMR to solve a purely mathematical problem in fewer steps than is possible classically. Our simple quantum computer can determine the type of an unknown function using fewer function 'calls' than is possible using a classical computer.

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A quantum computer is a device that processes information in a quantum-mechanically coherent fashion. In principle, it can exploit coherent quantum interference and entanglement to perform computations, such as factoring large numbers or searching an unsorted database, more rapidly than classical computers. Noise, decoherence, and manufacturing problems make constructing large scale quantum computers difficult. Ion traps and optical cavities offer promising experimental approaches, but no quantum algorithm has yet been implemented with those systems. On the other hand, because of their natural isolation from the environment, nuclear spins are particularly good 'quantum bits', and their use for quantum computation is possible by applying nuclear magnetic resonance (NMR) techniques in an unconventional manner. Here, we report on the experimental implementation of a quantum algorithm using NMR to solve a purely mathematical problem in fewer steps than is possible classically. Our simple quantum computer can determine the type of an unknown function using fewer function 'calls' than is possible using a classical computer.
Quantum computing shows great promise for the solution of many difficult problems, such as the simulation of quantum systems and the factorization of large numbers. While the theory of quantum computing is fairly well understood, it has proved difficult to implement quantum computers in real physical systems. It has recently been shown that nuclear magnetic resonance (NMR) can be used to implement small quantum computers using the spin states of nuclei in carefully chosen small molecules. Here we demonstrate the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions). This is the first successful implementation of a quantum algorithm on any physical system.
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.
Basic concepts of quantum theory of information, principles of quantum calculations and the possibility of creation on this basis unique on calculation power and functioning principle device, named quantum computer, are briefly reviewed. The main blocks of quantum logic, schemes of implementation of quantum calculations, as well as some known today effective quantum algorithms, called to realize advantages of quantum calculations upon classical, are concerned. Among them special place is taken by Shor's algorithm of number factorization, Grover's algorithm of unsorted database search and, finally, the most promising in application methods of quantum phenomena simulation, particularly quantum chaos. The most perspective methods of experimental realization of quantum computer, namely nuclear-magnetic resonance and trapped ions realizations, are discussed. Phenomena of decoherence, its influence on quantum computer stability and methods of quantum error correction are described.
Storing information in quantum mechanical degrees of freedom and processing it by unitary transformation promises a new class of computers that can efficiently solve problems for which no efficient classical algorithms are known. The most straightforward implementation of this type of information processing uses nuclear spins to store the information and nuclear magnetic resonance for processing it. We discuss the basics of quantum information processing by NMR, with an emphasis on two fields of research: the design and implementation of robust logical gate operations and the loss of quantum information, which is known as decoherence.
Quantum computation offers the extraordinary promise of solving mathematical and physical problems which are simply beyond the reach of classical computers. However, the experimental realization of quantum computers is extremely challenging, because of the need to initialize, manipulate and measure the state of a set of coupled quantum systems while maintaining fragile quantum coherence. In this thesis work, 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 = 3 × 5), 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. Furthermore, 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.
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.