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International journal of unconventional computing

Classical Computing in Nuclear Magnetic Resonance.

Marta Roselló-Merino, Matthias Bechmann, Angelika Sebald, Susan Stepney

Published Jan 1, 2010• 15 citations
OpenAlex

Abstract

As part of our longer term research objective of using the complex structure and dynamics of matter to perform non classical in materio computation, we show how to use NMR to perform classical computation. We describe three different approaches of using NMR to implement a single universal logic gate, and a circuit of these gates combined in parallel and in sequence that implement other logic gates, including various optimisations, and, in one case, a half-adder circuit. We then show how the three approaches are just specific instances of a more general approach set in a rich parameter space, and discuss how this parameter space might be exploited for more sophisticated computations.

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As part of our longer term research objective of using the complex structure and dynamics of matter to perform non classical in materio computation, we show how to use NMR to perform classical computation. We describe three different approaches of using NMR to implement a single universal logic gate, and a circuit of these gates combined in parallel and in sequence that implement other logic gates, including various optimisations, and, in one case, a half-adder circuit. We then show how the three approaches are just specific instances of a more general approach set in a rich parameter space, and discuss how this parameter space might be exploited for more sophisticated computations.
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We implement several non-binary logic systems using the spin dynamics of nuclear spins in nuclear magnetic resonance (NMR). The NMR system is a suitable test system because of its high degree of experimental control; findings from NMR implementations are relevant for other computational platforms exploiting particles with spin, such as electrons or photons. While we do not expect the NMR system to become a practical computational device, it is uniquely useful to explore strengths and weaknesses of unconventional computational approaches, such as non-binary logic.
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.
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 (NMR) has been widely used as a demonstrative medium for showcasing the ability for quantum computations to outperform classical ones. A large number of such experiments performed have been implementations of the Deutsch-Jozsa algorithm. It is known, however, that in some cases the Deutsch-Jozsa problem can be solved classically using as many queries to the black-box as in the quantum solution. In this paper we describe experiments in which we take the contrasting approach of using NMR as a classical computing medium, treating the nuclear spin vectors classically and utilising an alternative embedding of bits into the physical medium. This allows us to determine the actual Boolean function computed by the black-box for the n=1,2 cases, as opposed to only the nature (balanced or constant) as conventional quantum algorithms do. Discussion of these experiments leads to some clarification of the complications surrounding the comparison of different quantum algorithms, particularly black-box type algorithms.