imperialcollegelondon | The intention of this review was to present a limited number of quantum neural network
models as impartially as possible, with sufficient background material to be accessible
to anyone with a good understanding of quantum mechanics. Four models have been
examined and their properties discussed, with results of simulations by the authors
given with their interpretations. In three models simulations were performed to test
their effectiveness at standard neural network problems, and in each case the authors
report their models of QNNs performing better in some cases than comparable classical
neural networks.
It was the original intention of this dissertation, which the scope of necessary work
prevented, to produce a much more comprehensive review of QNNs and research into
them. In particular, several models exist which could not be studied here, including those described in work by Kak [26], Peruˇs [24], Zak and Williams [25], and Gupta and
Zia [27], and in further discussions by Ventura et al. EzhovVentura00b, Ventura00b,
Ezhov [30], and many others. In those models discussed, the review has aimed chiefly to
summarize the authors’ working and to report their claims for the model’s properties,
without commenting on further physical considerations which may cause difficulty for
the model. A deeper study of neural networks, including the operation of self-organizing
neural networks which through unsupervised learning can discover clusters of data independently,
is a possible extension in foundational material, as one of the possible
applications proposed by authors of QNNs not covered here.
None of the models discussed make extensive use of results in quantum information
theory, the most obvious being entanglement. Ventura and Martinez claim [7] to use
entanglement to maintain connections in their model, but this is not described or mentioned
in their most extensive paper on the subject [23]. It is possible that as many
of the authors cited are primarily experts in neural networks, they may have misused
results in quantum theory in constructing their models, particularly on the wavefunction
collapse, the no-cloning theorem, and the degree to which quantum parallelism may be
exploited; the author has chosen to err on the side of caution by not attempting to find
such errors, leaving that for an extension of this review after further study.
As a prognosis for the field of QNNs, this review is perhaps not promising, but strictly
incomplete and inconclusive. It is hoped that this review could form a useful base for
further study into quantum neural networks by familiarizing the reader with existing
models, which they may build upon or use as inspiration for another model. It should
be noted that most papers cited above date from 1996 to 2001, after which most authors
appeared to discontinue study, or at any rate ceased to publish on the topic. Whether
this is because of unpublished negative results, a loss of personal motivation, issues with
funding, or any other reason is not known, but it opens a conspicuous area for possible
study given an additional ten years of rapid research into quantum information theory.
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