Quantum Neural Computing Study
document is prepared for describing the basic idea of Quantum Neural Computing. It
has been modified since the
first version and will be better with new coming information. Please tell
me about your research and opinion.
Since Beniof [Ben82] and Feynman [Fey82] discovered the possibility of using quantum mechanical system for reasonable computing and Deutsch [Deu85] defined the first quantum computing model, the quantum computation have been developed as a interesting multidiscipline. Specially in recent years, the appearances of Shor's factoring algorithm [Sho94] and Grover's search algorithm [Grov96] speeded up the development in this area. A general review of the area is illustrated by Ekert and Deutsch´s article [Ekert98].
|2. Quantum Computer Simulation:
A review from Exeter University about QC simulation is unique, being the first available overview of progress in the field. As research interest in quantum computation grows, together with the number of field´s researchers, it seems certain that quantum computer simulators will play a major role in this research. [Wallace99]
Problems of Artificial Neural Networks
processing: the conventional learning is in terms of serial processing and this slowed
down the acceptance of a sampling operation that could achieve task-dependent selectivity
in a parallel processing environment [Gros98].
|4. Quantum Computing & Artificial Neural Networks
In the field of artificial neural networks (ANN), some pioneers introduced
quantum computation into analogous discussion such as quantum associative memory, parallel
learning and empirical analysis [Chr95, Kak95, Men95, Zar95, Beh96, Pru96, Val96]. They
constructed the foundation for further study of quantum computation in artificial neural
networks. Menneer developed her Ph. D. thesis in which deeply discussed the application of
quantum theory to ANN and demonstrated that QUANNs are more efficient than ANN for
classification tasks [Menn98]. Ventura and Martinez developed a quantum associative
memory, its structure and learning manner in quantum version [Ven98]. Weigang tried to
develop a parallel-SOM and mentioned the once learning manner in quantum computing
environment [Wei98]. He also proposed an Entanglement Neural Networks (ENN) on the base of
the quantum teleportation and its extension with intelligent sense. In AI and
quantum computing, there is more recent review from Hirsh et al. [Hir99, Hog99, Kak99,
Ven99]. The followings are main points of their researches.
In 1997, Lagaris, Likas and Fotiadis (Lagaris et al, 1997) developed Artificial Neural Networks for Solving Ordinary and Partial Differential Equations.
Purushothaman and Karayiannis (1998) publicated their paper "quantum neural networks (qnns) - inherently fuzzy feedforward neural networks" in IEEE Transactions on Neural Networks. It is also implimented in a classical ANN simulator - QNN/SNNS.
Bieberich (Bieberich, 1999) developed a paper about "Non-local quantum evolution of entangled ensemble states in neural nets and its significance for brain function and a theory of consciousness" .
Quantum dissipation and neural net dynamics are discussed by Pessa and Vitiello .
Holographic/Quantum Neural Technology (HNeT) Quantum mechanical concepts of
enfolding and quantum parallelism may be applied not only to energy and matter, but
describe how single neuron cells are capable of learning vast amounts of stimulus-response
information in real time - enfolding this information onto the same storage structures
(i.e. computer RAM). It is now realized and accepted that a single holographic/quantum
neural neuron cell is
Perus published his research at Neural Network World about his idea about Neural Networks as a basis for Quantum Associate Networks (Perus, 2000) and Quantum system can realize content_addressable associative memory (Perus and Dey, 2000).
Hu  developed a research about Quantum computation via Neural Networks applied to Image processing and pattern recognition. He proved that the error in measurement produced by quantum principle is half the error produced by a classical approach.
A neural-net-like model, which is realizable using quantum holography, is proposed for quantum associative me-mory and pattern recognition. This Hopfield-based math-ematical model/algorithm, translated to quantum formalism, has been successfully tested in computer simulations of concrete pattern-recognition applications [Peru and Bischof, 2002].
The paper "Quantum-implemented selective reconstruction of high-resolution images" proposes quantum image reconstruction. Input-triggered selection of an image among many stored ones, and its reconstruction if the input is occluded or noisy, has been simulated by a computer program implementable in a real quantum-physical system [Peru,2004].
|5. Entangled Neural Networks
Quantum teleportation is surprising the scientific community since it can
transmit an unknown quantum state following the no cloning principle of quantum mechanics
[Ben93, Bou97]. During teleportation, some limited information is transmitted in the
classical channel and the quantum state is transmitted in the quantum channel. Even though
the original quantum state can be reconstructed (with the price of destroying the original
state), nothing is learned during the transmission about the original state [Men98].
Considering the powerful learning ability of Artificial Neural Networks (ANN) [Hec90,
Hye94], Entangled Neural Networks (ENNs) are proposed in this sense to learn information
from inside and outside the system and to interfere and manipulate the huge amount of
knowledge using quantum parallelism. There is some interesting literature about the use of
ANN with quantum computing [Chr95, Kak95, Men95, Zar95, Beh96, Pru96, Val96, Men98, Van98,
Wei98], and especially, a more recent review from Hirsh et al. [Hir99, Hog99, Kak99,
Fourth International Conference on
COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE: Special Sessions on
Since this page has published, a lot of researchers sent e-mails to me for recommending their researches as J. Wallace, Z.Z. Hu, and M. Perus. The author thanks deeply for their support.
The research is supported in part by grant # 521442/97-4 from CNPq, Brazil.
Some information in this paper do not get the original author´s personal agreement. I got their main points just as the common manner to get the the reference from science community. If there is any problem, please tell me.
[Bar96] Barenco, Adriano, "Quantum physics and
computers", Contemporary Physics, vol.37, no. 5, pp.375-89, 1996.
[Bie99] Bieberich, E. "Non-local quantum
evolution of entangled ensemble states in neural nets and its significance for brain
function and a theory of consciousness", 1999, quant-ph/9906011.
[Lag97] Lagaris, I. E., A. Likas, D. I. Fotiadis
"Artificial Neural Network Methods in Quantum Mechanics", Comput.Phys. Commun.
104 (1997) 1-14.
[Hu2001] Hu, Z.Z., Quantum computation
via Neural Networks applied to Image processing and pattern recognition. PhD
thesis at the University of Western Sydney, Australia.
[Perus97] M. Perus, Mind: neural computing plus quantum consciousness, in Mind Versus Computer, Edited by M. Gams, M. Paprzychi and X. Wu, by IOS press, pp. 156-170, 1997
[Perus98] Common mathematical foundations of neural and quantum informatics, in Zeitschrift Fur Angewandte Mathematik und Mechanik, Vol. 78 (1998), Suppl. 1, p9. 23-26.
[Perus2000] Neural Networks as a basis for Quantum Associate Networks, in Neural Network World, vol. 10, n. 6, pp.1001-1013, 2000.
[Perus and Dey, 2000] Perus and Dey, Quantum system can realize content_addressable associative memory, in Applied Mathematics Letters, vol. 13, no. 8, pp.31-36, Pergamon, 2000.
[Perus and Bischof, 2002].Quantum-wave pattern recognition: from simulations towards implementation, Comput. Intellig. and Natural Comp. 2002 conf. in North Carolina.
Pessa, E, G. Vitiello: "Quantum
dissipation and neural net dynamics", 1999, quant-ph/9912070.
Quantum-implemented selective reconstruction of high-resolution images,
Quantum Physics, abstract
[Ven98] Ventura, D. and T. Martinez, "Quantum
Associative Memory", preprint submitted to IEEE Transactions on Neural
Initial publication : 1999; Last updated: 06-06-2003.