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International Joint Conference on Neural Networks (IJCNN)

Quantum associative memory with exponential capacity

Dan A. Ventura, Tony R. Martinez

Published Nov 27, 2002• 47 citations
Publisher

Abstract

Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts by taking advantage of quantum parallelism. The unique characteristics of quantum theory may also be used to create a quantum associative memory with a capacity exponential in the number of neurons. This paper covers necessary high-level quantum mechanical ideas and introduces a simple quantum associative memory. Furthermore, it provides discussion, empirical results and directions for future work.

DOI
10.1109/ijcnn.1998.682319

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Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts by taking advantage of quantum parallelism. The unique characteristics of quantum theory may also be used to create a quantum associative memory with a capacity exponential in the number of neurons. This paper covers necessary high-level quantum mechanical ideas and introduces a simple quantum associative memory. Furthermore, it provides discussion, empirical results and directions for future work.
Quantum associative memory (QuAM) in the domain of quantum computation is a model with a capacity exponential in the number of neurons. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem where the classical data must be read and after the measurement the superposition collapses. Most quantum machine learning algorithms including quantum associative memory suffer from the input destruction problem. The efficient preparation of data is possible in part for spares data. However, the input destruction problem is not solved till today, and usually theoretical speed ups are analyzed by ignoring the input problem, which is the main bottleneck for data encoding. The naming of the phases is in analogy to a living organism that prepares itself during the sleep for an active day. The advantage of quantum approach is present in the active phase.
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.
An approach to constructing an artificial quantum associative memory based on entanglement (QuEAM) is discussed. The QuEAM is an exponential increase in the capacity of the memory when compared to classical associative memories such as the Hopfield network. According to the characteristics of amount of entanglement, the study algorithm based on Grover's well-known algorithm is locally magnified the probability amplitude for the qubit. The basic principle of entangled states is discussed. Concrete examples illustrating the properties of the proposed model are also presented.
Abstract This paper discusses an approach to constructing an artificial quantum associative memory (QuAM). The QuAM makes use of two quantum computational algorithms, one for pattern storage and the other for pattern recall. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. Further, the paper argues for considering pattern recall as a non-unitary process and demonstrates the utility of non-unitary operators for improving the pattern recall performance of the QuAM. 1.
We describe a quantum algorithm for computing the intersection of two sets and its application to associative memory. The algorithm is based on a modification of Grover's quantum search algorithm (Grover, 1996). We present algorithms for pattern retrieval, pattern completion, and pattern correction. We show that the quantum associative memory can store an exponential number of memories and retrieve them in sub-exponential time. We prove that this model has advantages over known classical associative memories as well as previously proposed quantum models.