{"title":"Quantum Enhanced Correlation Matrix Memories via States Orthogonalisation","authors":"Mario Mastriani, Marcelo Naiouf","volume":80,"journal":"International Journal of Nuclear and Quantum Engineering","pagesStart":1127,"pagesEnd":1133,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9996640","abstract":"<p>This paper introduces a Quantum Correlation Matrix Memory (QCMM) and Enhanced QCMM (EQCMM), which are useful to work with quantum memories. A version of classical Gram-Schmidt orthogonalisation process in Dirac notation (called Quantum Orthogonalisation Process: QOP) is presented to convert a non-orthonormal quantum basis, i.e., a set of non-orthonormal quantum vectors (called qudits) to an orthonormal quantum basis, i.e., a set of orthonormal quantum qudits. This work shows that it is possible to improve the performance of QCMM thanks QOP algorithm. Besides, the EQCMM algorithm has a lot of additional fields of applications, e.g.: Steganography, as a replacement Hopfield Networks, Bilevel image processing, etc. Finally, it is important to mention that the EQCMM is an extremely easy to implement in any firmware.<\/p>\r\n","references":"[1]\tR. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21(1982)467-488.\r\n[2]\tR. P. Feynman, Quantum Mechanical Computers, Found. Phys. 16(1986)507-531.\r\n[3]\tD. Deutch, Quantum computational networks, Proc. Roy. Soc. Lond A439(1992)553-558.\r\n[4]\tA. Yu. Vlasov, Quantum computations and images recognition, quant- ph\/9703010; Analogues quantum computers for data analysis quant- ph\/9802028.\r\n[5]\tE. Knill, R. La\ufb02amme and G. J. Milburn. A scheme for e\ufb03cient quantum computation with linear optics, Nature 409(2001)46-57.\r\n[6]\tS. Haykin, Neural Networks: A Comprehensive Foundation, Macmillan, New York (2000).\r\n[7]\tM. Mastriani, \"Self-Restorable Stochastic Neuro-Estimation using Forward-Propagation Training Algorithm,\u201d Proc. of INNS, Portland, OR, 1, 404-411 (1993a).\r\n[8]\tM. Mastriani, \"Self-Restorable Stochastic Neurocontrol using Back-Propagation and Forward-Propagation Training Algorithms,\u201d Proc. of ICSPAT, Santa Clara, CA, 2, 1058-1071 (1993b).\r\n[9]\tM. Mastriani, \"Pattern Recognition Using a Faster New Algorithm for Training Feed-Forward Neural Networks,\u201d Proc. of INNS, San Diego, CA, 3, 601-606 (1994a).\r\n[10]\tM. Mastriani, \"Predictor of Linear Output,\u201d Proc. IEEE Int. Symposium on Industrial Electronics, Santia-go, Chile, 269-274 (1994b).\r\n[11]\tM. Mastriani, \"Predictor-Corrector Neural Network for doing Technical Analysis in the Capital Market,\u201d Proc. AAAI International Symposium on Artificial Intelligence, Monterrey, M\u00e9xico, 49-58 (1994c).\r\n[12]\tD. J. Willshaw, and C. von der Malsburg, \"How patterned neural connections can be set up by self-organization,\u201d Proc. of the Royal Society of London, Series B 194, 431-445 (1976).\r\n[13]\tT. Kohonen, \"Physiological interpretation of the self-organizing map algorithm.\u201d Neural Networks 6, 895-905 (1993).\r\n[14]\tG. Palm, Neural Assemblies: An Alternative Approach, New York: Springer-Verlag (1982).\r\n[15]\tD. J. Willshaw, and \"et. al\u201d, \"Non-holographic associative memory,\u201d Nature (London) 222, 960-962 (1969).\r\n[16]\tE. B. Baum, F. Wilczek, and J. Moody, \"Internal Representation for Associative Memories\u201d, Biological Cybernetics, 1998, Vol. 59, pp. 217-228.\r\n[17]\tS. Hobson, and J. Austin, \"Improved Storage Capacity in Correlation Matrix Memories Storing Fixed Weight Codes,\" in 19th International Conference on Artificial Neural Networks: Part I, Limassol, 2009, pp. 728-736.\r\n[18]\tD. Kustrin, and J. Austin, \"Connectionist Propositional Logic: A Simple Correlation Matrix Memory Based Reasoning System,\" in Emergent neural computational architectures based on neuroscience: towards neuroscience-inspired computing, Stefan Wermter, Jim Austin, and David Willshaw, Eds. New York, United States of America: Springer-Verlag, 2001, pp. 534-546.\r\n[19]\tM. Turner, and J. Austin, \"Matching performance of binary correlation matrix memories,\" Transactions of the Society for Computer Simulation International, vol. 14, no. 4, pp. 1637-1648, Dec. 1997.\r\n[20]\tT. Kohonen, \"Correlation Matrix Memories.\u201d IEEE Trans. on Computers, C-21, 353-359 (1972).\r\n[21]\tN. Burles. Quantum parallel computation with neural networks. Master's thesis, University of York, 2010.\r\n[22]\tM. A. Nielsen and I. L. Chuang, Quantum computation and quantum information. Cambridge: Cambridge UP, 2000.\r\n[23]\tM. Mastriani, and M. Naiouf, \"Enhanced Gram-Schmidt Process for Improving the Stability in Signal and Image Processing\u201d, WSEAS Transactions on Signal Processing, ID: 5714-124.\r\n[24]\tM. Mastriani, \"Enhanced Boolean Correlation Matrix Memory\", (RNL02), X RPIC Reuni\u00f3n de Trabajo en Procesamiento de la Informaci\u00f3n y Control, 8 al 10 de Octubre 2003, San Nicol\u00e1s, Buenos Aires, Argentina, vol. 2, pp. 470-473.\r\n[25]\tM. Mastriani, \"Systholic Boolean Orthonormalizer Network in Wavelet Domain for Microarray Denoising,\u201d International Journal of Signal Processing, Volume 2, Number 4, pp.273-284, 2005.\r\n[26]\tM. Mastriani, \"Denoising and Compression in Wavelet Domain via Projection onto Approximation Coefficients,\u201d International Journal of Signal Processing, Volume 5, Number 1, pp.20-30, 2008.\r\n[27]\tM. Mastriani, \"Systholic Boolean Orthonormalizer Network in Wavelet Domain for SAR Image Despeckling\u201d, WSEAS Transactions on Signal Processing, ID: 5714-125.\r\n[28]\tM. Mastriani, \"New Tool for Boolean Signal Processing\u201d, WSEAS Transactions on Signal Processing, ID: 5714-126.\r\n[29]\tM. Mastriani, \"Enhanced Boolean Correlation Matrix Memory\u201d, WSEAS Transactions on Signal Processing, ID: 5714-127.\r\n[30]\tM. Mastriani, \"Fast Cosine Transform to increase speed-up and efficiency of Karhunen-Lo\u00e8ve Transform for lossy compression of SAR imagery\u201d, WSEAS Transactions on Signal Processing, ID: 5714-160.\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 80, 2013"}