dorsal/arxiv
View SchemaQuantum Neural Networks
| Authors | Sanjay Gupta, R. K. P. Zia |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201144 |
| URL | https://arxiv.org/abs/quant-ph/0201144 |
Abstract
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called \emph{Quantum Neural Networks (QNNs)} is defined, building on Deutsch's model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schr\"{o}dinger's equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural networks. QNNs of polylogarithmic size and polylogarithmic depth can solve the problems in \NC, the class of problems with theoretically fast parallel solutions. Thus, the new model may indeed provide an approach for building scalable parallel computers.
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"abstract": "This paper initiates the study of quantum computing within the constraints of\nusing a polylogarithmic ($O(\\log^k n), k\\geq 1$) number of qubits and a\npolylogarithmic number of computation steps. The current research in the\nliterature has focussed on using a polynomial number of qubits. A new\nmathematical model of computation called \\emph{Quantum Neural Networks (QNNs)}\nis defined, building on Deutsch\u0027s model of quantum computational network. The\nmodel introduces a nonlinear and irreversible gate, similar to the speculative\noperator defined by Abrams and Lloyd. The precise dynamics of this operator are\ndefined and while giving examples in which nonlinear Schr\\\"{o}dinger\u0027s\nequations are applied, we speculate on its possible implementation. The many\npractical problems associated with the current model of quantum computing are\nalleviated in the new model. It is shown that QNNs of logarithmic size and\nconstant depth have the same computational power as threshold circuits, which\nare used for modeling neural networks. QNNs of polylogarithmic size and\npolylogarithmic depth can solve the problems in \\NC, the class of problems with\ntheoretically fast parallel solutions. Thus, the new model may indeed provide\nan approach for building scalable parallel computers.",
"arxiv_id": "quant-ph/0201144",
"authors": [
"Sanjay Gupta",
"R. K. P. Zia"
],
"categories": [
"quant-ph"
],
"title": "Quantum Neural Networks",
"url": "https://arxiv.org/abs/quant-ph/0201144"
},
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