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The quest for a Quantum Neural Network

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Abstract

With the overwhelming success in the field of quantum information in the last decades, the ‘quest’ for a Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. This article presents a systematic approach to QNN research, which so far consists of a conglomeration of ideas and proposals. Concentrating on Hopfield-type networks and the task of associative memory, it outlines the challenge of combining the nonlinear, dissipative dynamics of neural computing and the linear, unitary dynamics of quantum computing. It establishes requirements for a meaningful QNN and reviews existing literature against these requirements. It is found that none of the proposals for a potential QNN model fully exploits both the advantages of quantum physics and computing in neural networks. An outlook on possible ways forward is given, emphasizing the idea of Open Quantum Neural Networks based on dissipative quantum computing.

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Notes

  1. The only systematic review in the field of QNNs was given in 2000 by Ezhov and Ventura [22] (not counting the brief overview of the different types of implementations of QNNs in Oliveira et al. [19]). To our knowledge, there is no recent comprehensive review.

  2. The Hamming distance is the number of state flips to turn one binary string into another one, thus measuring the overlap between two binary strings [30].

  3. A problem is linearly separable if the respective outputs in phase space can be divided by a hyperplane. Perceptrons can only compute linear separable problems.

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Acknowledgments

This work is based upon research supported by the South African Research Chair Initiative of the Department of Science and Technology and National Research Foundation.

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Authors and Affiliations

  1. Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, KwaZulu-Natal, 4001, South Africa

    Maria Schuld, Ilya Sinayskiy & Francesco Petruccione

  2. National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, 4001, South Africa

    Ilya Sinayskiy & Francesco Petruccione

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  1. Maria Schuld
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Correspondence to Maria Schuld.

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Schuld, M., Sinayskiy, I. & Petruccione, F. The quest for a Quantum Neural Network. Quantum Inf Process 13, 2567–2586 (2014). https://doi.org/10.1007/s11128-014-0809-8

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