Quantum neural network

Bioelectrochemistry and Bioenergetics, 1999

Inspired by the dissipative quantum model of brain, we model the states of neural nets in terms of collective modes by the help of the formalism of Quantum Field Theory. We exhibit an explicit neural net model which allows to memorize a sequence of several informations without reciprocal destructive interference, namely we solve the overprinting problem in such a way last registered information does not destroy the ones previously registered. Moreover, the net is able to recall not only the last registered information in the sequence, but also anyone of those previously registered.

NeuroQuantology, 2016

The current work addresses quantum machine learning in the context of Quantum Artificial Neural Networks such that the networks' processing is divided in two stages: the learning stage, where the network converges to a specific quantum circuit, and the backpropagation stage where the network effectively works as a self-programing quantum computing system that selects the quantum circuits to solve computing problems. The results are extended to general architectures including recurrent networks that interact with an environment, coupling with it in the neural links' activation order, and self-organizing in a dynamical regime that intermixes patterns of dynamical stochasticity and persistent quasiperiodic dynamics, making emerge a form of noise resilient dynamical record.

2022

To address Quantum Artificial Neural Networks as quantum dynamical computing systems, a formalization of quantum artificial neural networks as dynamical systems is developed, expanding the concept of unitary map to the neural computation setting and introducing a quantum computing field theory on the network. The formalism is illustrated in a simulation of a quantum recurrent neural network and the resulting field dynamics is researched upon, showing emergent neural waves with excitation and relaxation cycles at the level of the quantum neural activity field, as well as edge of chaos signatures, with the local neurons operating as far-from-equilibrium open quantum systems, exhibiting entropy fluctuations with complex dynamics including complex quasiperiodic patterns and power law signatures. The implications for quantum computer science, quantum complexity research, quantum technologies and neuroscience are also addressed.

Quantum neural computation employs quantum computational circuits that consist of chains of conditional unitary operators that follow the network's neural links leading to entanglement between the local neuron-level computation and the network. When such quantum computational circuits are applied iteratively, instead of an input and output density, we have a sequence of density operators, with the transition from one density to another resulting from a form of unitary quantum map. It has been shown that these unitary quantum neural maps lead to complex emergent dynamics at the level of relevant quantum averages. The present work expands the research on quantum neural maps combining it with quantum stochastic processes theory, introducing the concept of a quantum stochastic neural map, resulting from a coupling to an external noise source. The unitary and stochastic maps are implemented for a quantum recurrent neural network, showing evidence of complex emergent dynamics, including, in the case of the stochastic map, fractal attractors that leave a signature at the level of the energy versus mutual information plots, as well as local (neuron-level) entropy resilient dynamics, where each neuron, as an open computing unit, exhibits dissipation but does not reach full entanglement-related decoherence.

Quantum computer science in combination with paradigms from computational neuroscience, specifically those from the field of artificial neural networks, seems to be promising for providing an outlook on a possible future of artificial intelligence. Within this elaboration, a quantum artificial neural network not only apportioning effects from quantum mechanics simulated on a von Neumann computer is proposed, but indeed for being processed on a quantum computer. Sooner or later quantum computers will replace classical von Neumann machines, which has been the motivation for this research. Although the proposed quantum artificial neural network is a classical feed forward one making use of quantum mechanical effects, it has, according to its novelty and otherness, been dedicated an own paper. Training such can only be simulated on von Neumann machines, which is pretty slow and not practically applicable (but nonetheless required for proofing the theorem), although the latter ones may be used to simulate an environment suitable for quantum computation. This is what has been realized during the SHOCID (Neukart, 2010) project for showing and proofing the advantages of quantum computers for processing artificial neural networks.

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.

Information Sciences, 2000

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. 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 combines two quantum computational algorithms to produce a quantum associative memory. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. The paper covers necessary high-level quantum mechanical ideas and introduces a quantum associative memory, a small version of which should be physically realizable in the near future.

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.

Information Sciences, 2000

We explore by simulation ways in which an array of quantum dot molecules could serve as a quantum neural computer. First, we show that a single quantum dot molecule evolving in real time can act as a recurrent temporal quantum neural network. Inputs are prepared by ®xing the initial states of a quantum dot molecule, and outputs determined by reading its value at a given time T later. The nodes of the network are the instantaneous states of the molecule at successive time slices. The nodes interact indirectly through their mutual interaction with local and phononic modes of the substrate. These modes can be preferentially excited optically, and, therefore, controlled externally. The number of excitations can thus be used as trainable``weight'' parameters for a neural network. This network is shown to perform classical logic gates. By preparing the input state as a superposition state, multiple inputs can be encoded as a single initial state. Second, we simulate the possibility of a spatial, rather than temporal, design, as a Hop®eld net. The network consists of a regular array of quantum dot molecules on a suitable substrate. The molecules interact indirectly as before, and, now, with each other directly through Coulombic interactions. Both of the quantum networks have none of the``wiring problems'' of traditional neural nets: the necessary connections are supplied by the physical system itself. Computation is performed by the intrinsic physics of the physical system. The long range character of the phononic interactions takes the net beyond traditional local connectionist structures. The hypothesized increase in

International Journal of Modern Physics B, 2000

In this report we will consider some recent developments of the quantum model of brain which include dissipative dynamics and time dependent frequency of the electric dipole wave quanta (dwq) . The dissipative quantum model of brain has been recently investigated also in relation with the possibility of modeling neural networks exhibiting collective dynamics and long range correlations among the net units. The study of such a quantum dynamical features for neural nets is of course of great interest either in connection with computational neuroscience, either in connection with quantum computational strategies based on quantum evolution (quantum computation). On the other hand, further developments of the quantum model of brain, on which here we do not report, show attractive features also related with the rôle of microtubules in brain activity .

2018

In source memory studies, a decision-maker is concerned with identifying the context in which a given episodic experience occurred. A common paradigm for studying source memory is the `three-list' experimental paradigm, where a subject studies three lists of words and is later asked whether a given word appeared on one or more of the studied lists. Surprisingly, the sum total of the acceptance probabilities generated by asking for the source of a word separately for each list (`list 1?', `list 2?', `list 3?') exceeds the acceptance probability generated by asking whether that word occurred on the union of the lists (`list 1 or 2 or 3?'). The episodic memory for a given word therefore appears over distributed on the disjoint contexts of the lists. A quantum episodic memory model [QEM] was proposed by Brainerd, Wang and Reyna (2013) to explain this type of result. In this paper, we apply a Hamiltonian dynamical extension of QEM for over distribution of source memor...

International Journal of Modern Physics B, 1995

The quantum model of the brain proposed by Ricciardi and Umezawa is extended to dissipative dynamics in order to study the problem of memory capacity. It is shown that infinitely many vacua are accessible to memory printing in a way that in sequential information recording the storage of a new information does not destroy the previously stored ones, thus allowing a huge memory capacity. The mechanism of information printing is shown to induce breakdown of time-reversal symmetry. Thermal properties of the memory states as well as their relation with squeezed coherent states are finally discussed.

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.

1999