High-Capacity Quantum Associative Memories

1998

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. Further, it provides discussion, empirical results and directions for future work.

Physical Review Letters, 2006

Qubit networks with long-range interactions inspired by the Hebb rule can be used as quantum associative memories. Starting from a uniform superposition, the unitary evolution generated by these interactions drives the network through a quantum phase transition at a critical computation time, after which ferromagnetic order guarantees that a measurement retrieves the stored pattern. The maximum memory capacity of these qubit networks is reached at a memory density alpha=p/n=1.

On this paper, we briefly analyze and compare some models of quantum artificial neural networks. Quantum operators must be linear ones; we verify that no unitary operators are used in two models of quantum perceptron. We also analyze a model of quantum weightless neural network and a quantum complex neural network. These models have quantum architecture and learning, but we show that they use nonlinear operators in the learning process. This study, toward a comparative method, tries to clarify important aspects in models of quantum neural networks as well as understand more its operation.

The 2012 International Joint Conference on Neural Networks (IJCNN), 2012

As computers approach the physical limits of information storable in memory, new methods will be needed to further improve information storage and retrieval. We propose a quantum inspired vector based approach, which offers a contextually dependent mapping from the subsymbolic to the symbolic representations of information. If implemented computationally, this approach would provide exceptionally high density of information storage, without the traditionally required physical increase in storage capacity. The approach is inspired by the structure of human memory and incorporates elements of Gärdenfors' Conceptual Space approach and Humphreys et al.'s matrix model of memory. Kitto, K., Bruza, P., & Gabora, L. (2012). A quantum information retrieval approach to memory. Proc International Joint Conf on Neural Networks, (pp. 932-939). June 10-15, Brisbane, Australia, IEEE Computational Intelligence Soc.

The model of quantum associative memories proposed here is quietly similar to that of Rigui Zhou \etal \cite{zhou2012} based on quantum matrix with binary decision diagram and nonlinear search algorithm put forth by David Rosenbaum \cite{Rosenbaum2010} and Abrams and Llyod \cite{Abrams1998} respectively. Our model that simplifies and generalizes that of Ref. \cite{zhou2012}, gives the possibility to retrieve one of the desired states in multi-values retrieving, when a measure on the first register is done. If $n$ is the number of qubit of the first register, $p\leq2^n$ the number of stored patterns, $q\leq p$ the number of stored patterns if the values of $t$ are known (i.e., $t$ qubits have been measured or are already be disentangled to others, or the oracle acts on a subspace of $(n-t)$ qubits), $m\leq q$ the number of values $x$ for which $f(x)=1$, $c=\mathtt{ceil}(\log_2 {q})$ the least integer greater or equal to $\log_2{q}$, and $r=\mathtt{int} (\log_2 {m})$ the integer part ...

Procedia Engineering, 2014

The advances that have been achieved in quantum computer science to date, slowly but steadily find their way into the field of artificial intelligence. Specifically the computational capacity given by quantum parallelism, resulting from the quantum linear superposition of quantum physical systems, as well as the entanglement of quantum bits seem to be promising for the implementation of quantum artificial neural networks. Within this elaboration, the required information processing from bit-level up to the computational neuroscience-level is explained in detail, based on the combined research in the fields of quantum physics and artificial neural systems.

In this paper we consider a Quantum computational algorithm that can be used to determine (probabilistically) how close a given signal is one of a set of previously observed signals stored in the state of a quantum neurocomputional machine. The realization of a new quantum algorithm for factorization of integers by Shor and its implication to cryptography has created a rapidly growing field of investigation. Although no physical realization of quantum computers is available, a number of softwar systems simulating a quantum computation process exist. In light of the rapidly increasing power of desktop computers and their ability to carry out these simulations, it is worthwhile to investigate possible advantages as well as realizations of quantum algorithms in signal processing applications. The algorithm presented in this paper offers a glimpse of the potentials of this approach. Neural Networks (NN) provide a natural paradigm for parallel and distributed processing of a wide class of signals. Neural Networks within the context of classical computation have been used for approximation and classification tasks with some success. In this paper we propose a model for Quantum Neurocomputation (QN) and explore some of its properties and potential applications to signal processing in an information-theoretic context. A Quantum Computer can evolve a coherent superposition of many possible input states, to an output state through a series of unitary transformations that simultaneously affect each element of the superposition. This construction generates a massively parallel data processing system existing within a single piece of hardware. Our model of QN consists of a set of Quantum Neurons and Quantum interconnections. Quantum neurons represent a normalized element of the n-dimensional Hilbert space -a state of a finite dimensional quantum mechanical system. Quantum connections provide a realization of probability distribution over the set of state that combined with the Quantum Neurons provide a densit matrix representation of the system. A second layer with a similar architecture interrogates the system through a series of random state descriptions to obtain an average state description. We discuss the application of this paradigm to the quantum analog of independent states using the quantum version of the Kullback-Leibler distance.

2012

A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the very same error rate as the optimal (programmable) discrimination machine for any size of the training set. At variance with the latter, this machine can be used an arbitrary number of times without retraining. Its required (classical) memory grows only logarithmically with the number of training qubits, while (asymptotically) its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an "estimate-and-discriminate" machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.

The emerging research area of a quantum-inspired computing has been applied to various¯eld such as computational intelligence, and showed its superior abilities. However, most existing researches are focused on theoretical simulations, and have not been implemented in systems under practical environment. For human-robot communication, associative memory becomes essential for multi-modal communication. However, it always su®ers from low memory capacity and recall reliability. In this paper, we propose a quantum-inspired bidirectional associative memory with fuzzy inference. We show that fuzzy inference satis¯es basic postulates of quantum mechanics, but also learning algorithm for weight matrix in associative memory. In addition, we construct a communication system with robot partner using proposed model. This is the¯rst successful attempt to overcome conventional problems in associative memory model with a robot application.

2008

This paper studies neural structures with weights that follow the model of the quantum harmonic oscillator. The proposed neural networks have stochastic weights which are calculated from the solution of Schrödinger's equation under the assumption of a parabolic (harmonic) potential. These weights correspond to diffusing particles, which interact with each other as the theory of Brownian motion (Wiener process) predicts. It is shown that conventional neural networks and learning algorithms based on error gradient can be conceived as a subset of the proposed quantum neural structures. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of patterns storage capacity (number of attractors).