Pattern Recognition with Quantum Neural Networks

New model of quantum neural nework able to solve classification problems is presented. It is based on the extention of the model of quantum associative memory [1] and also utilizes Everett's interpretation of quantum mechanics [2-4]. For presented model not neural weights but quantum entanglement is responsible for associations between input and output patterns. Distributed form of queries permits the system to generalize. Spurious memory trick is used to control the number of Grover's iterations which is necessary to transform initial quantum state into the state which can give correct classification in most measurements. Numerical modelling of counting problem illustrates model's behavior and its potential benefits.

[1]  Tony R. Martinez,et al.  A Quantum Associative Memory Based on Grover's Algorithm , 1999, ICANNGA.

[2]  Igor Aleksander,et al.  CONNECTIONISM OR WEIGHTLESS NEUROCOMPUTING , 1991 .

[3]  A. A. Ezhov,et al.  Object Generation with Neural Networks (When Spurious Memories are Useful) , 1996, Neural Networks.

[4]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[5]  Antti Hautamäki,et al.  Brain, mind and physics , 1997 .

[6]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[7]  R. Feynman.  Quantum mechanical computers , 1986 .

[8]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[9]  T. Martinez,et al.  Initializing the Amplitude Distribution of a Quantum State , 1998, quant-ph/9807054.

[10]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[11]  D. Deutsch.  The fabric of reality , 1997, The Art of Political Storytelling.

[12]  Mitja Perus,et al.  Neuro-Quantum Parallelism in Brain-Mind and Computers , 1996, Informatica.

[13]  Dan Ventura,et al.  Quantum Neural Networks , 2000 .

[14]  Subhash Kak.  The Initialization Problem in Quantum Computing , 1998 .

[15]  Dan Ventura,et al.  Quantum associative memory with distributed queries , 2000, Inf. Sci..