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International Conference on Intelligent Networks and Intelligent Systems

Quantum Associative Memory Based on Subspace Projection

Lingxiang Zheng

Published Nov 1, 2008• 0 citations
Publisher

Abstract

To study the biological associative phenomena, we propose a novel quantum associative neural network model based on the subspace projection transformation of the quantum system. The patterns are encoded into a set of independent quantum state and iteratively stored into the quantum associative memory. The information retrieval is an action of projection transformation and follows a POVM measurement. Computer simulations show that it exhibits good associative ability. It can associatively recognize the face with different expression from a set of face images. In addition, the model can dramatically improve the storage capacity and process speed compared with the classical neural network model due to the quantum techniques. Compared with previous quantum associative memory models, our model can memorize and retrieval nonorthogonal quantum patterns with good performance.

DOI
10.1109/icinis.2008.78

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To study the biological associative phenomena, we propose a novel quantum associative neural network model based on the subspace projection transformation of the quantum system. The patterns are encoded into a set of independent quantum state and iteratively stored into the quantum associative memory. The information retrieval is an action of projection transformation and follows a POVM measurement. Computer simulations show that it exhibits good associative ability. It can associatively recognize the face with different expression from a set of face images. In addition, the model can dramatically improve the storage capacity and process speed compared with the classical neural network model due to the quantum techniques. Compared with previous quantum associative memory models, our model can memorize and retrieval nonorthogonal quantum patterns with good performance.
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To simulate the brain functions,a quantum associative memory combined with information preprocessing by a sparse coding model is presented. The sparse coding scheme is used to simulate the information transformation from retina up to primary visual cortex (V1) along the visual path and the quantum associative memory is used to simulate the pattern processing functions of the brain such as the pattern storing,forgetting and retrieving. Experimental results show that the model exhibits good associative ability on face recognition. Considering the huge storage capacity,mass parallel-distributed processing ability and oscillatory phenomena of the quantum system,this model might be a biological plausible implementation.
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We review our models of quantum associative memories that represent the “quantization” of fully coupled neural networks like the Hopfield model. The idea is to replace the classical irreversible attractor dynamics driven by an Ising model with pattern-dependent weights by the reversible rotation of an input quantum state onto an output quantum state consisting of a linear superposition with probability amplitudes peaked on the stored pattern closest to the input in Hamming distance, resulting in a high probability of measuring a memory pattern very similar to the input. The unitary operator implementing this transformation can be formulated as a sequence of one-qubit and two-qubit elementary quantum gates and is thus the exponential of an ordered quantum Ising model with sequential operations and with pattern-dependent interactions, exactly as in the classical case. Probabilistic quantum memories, that make use of postselection of the measurement result of control qubits, overcome the famed linear storage limitation of their classical counterparts because they permit to completely eliminate crosstalk and spurious memories. The number of control qubits plays the role of an inverse fictitious temperature. The accuracy of pattern retrieval can be tuned by lowering the fictitious temperature under a critical value for quantum content association while the complexity of the retrieval algorithm remains polynomial for any number of patterns polynomial in the number of qubits. These models thus solve the capacity shortage problem of classical associative memories, providing a polynomial improvement in capacity. The price to pay is the probabilistic nature of information retrieval.