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Physical Review Letters

NMR Implementation of a Parallel Search Algorithm

Anatoly K. Khitrin, Vladimir L. Ermakov, B. M. Fung

Published Dec 19, 2002• 16 citations
Publisher

Abstract

Recently it has been shown that the dynamics of a cluster of dipolar-coupled spins can be manipulated to store and process a large amount of information in a parallel way [Chem. Phys. Lett. 360, 161 (2002)]]. Here it is further demonstrated that it is possible to realize a cascade of parallel bitwise operations on a spin cluster so that an algorithm of parallel search can be experimentally implemented by means of nuclear magnetic resonance.

DOI
10.1103/physrevlett.89.277902

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Recently it has been shown that the dynamics of a cluster of dipolar-coupled spins can be manipulated to store and process a large amount of information in a parallel way [Chem. Phys. Lett. 360, 161 (2002)]]. Here it is further demonstrated that it is possible to realize a cascade of parallel bitwise operations on a spin cluster so that an algorithm of parallel search can be experimentally implemented by means of nuclear magnetic resonance.
Information storage and database search are attractive areas in the field of nuclear magnetic resonance. Among the notable works reported earlier, an implementation of a parallel search algorithm in a dipolar coupled spin cluster has gained considerable attention [A. Khitrin, V. L. Ermakov, and B. M. Fung, Phys. Rev. Lett. 89, 277902 (2002)]. In this paper, we propose and exemplify that spatial encoding can be successfully utilized in realizing such parallel algorithms. We also introduce an improved protocol of the parallel search algorithm, which can be realized using spatial encoding. The methods have been demonstrated to perform a search operation using 215 bits.
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.
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.
An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of NNN items with O(phN)O(\sqrt{\mathit{ph}N})O(phN​) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.
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.
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.