Wednesday, January 27, 2016

no help with my IQ-200+ wild goose chase hair, so I'll wrap it up with this superb survey...,

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.