Neural networks with c-NOT gated nodes

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.

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

1997

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. Choosing the best weights for a neural network is a time consuming problem that makes the harnessing of this "quantum parallelism" appealing. This paper briefly covers necessary high-level quantum theory and introduces a model for a quantum neuron.

This study concerns with the dynamics of a quantum neural network unit in the context of simple neural computing tasks. More specifically, we examine an interacting spin model chosen as a quantum percerpton and examine its dynamics as closed and open quantum systems. We adopt a collisional model enables examining both Markovian and non-Markovian dynamics of the proposed quantum system. We show that our quantum perceptron model has a stable output quantum state in contact with a dissipative quantum information environment. We perform numerical simulations to the proposed system and compare the dynamics in the presence and absence of quantum memory effects. With our findings we conclude that our quantum perceptron model is suitable for implementing general neural computing tasks when immersed in a Markovian information environment and quantum memory effects are not desirable since they cause complications on the stability of the output state.

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.

International Journal of Modern Physics C, 2003

The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of the brain neurons, is actively discussed in the last years. Positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied {\it in vivo} on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in generation of pleasure and in development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a {\it quantum} system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental ({\it in vivo}) indication in the favour of the quantum (at least partially) nature of the brain neurons activity.

ACM Computing Surveys

In recent years, Quantum Computing witnessed massive improvements in terms of available resources and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn the scientific community’s interest since the late 80s. In such a context, we propose our contribution. First, we introduce basic concepts related to quantum computations, and then we explain the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms. Finally, we gather, compare and analyze the current state-of-the-art concerning Quantum Perceptrons and Quantum Neural Networks implementations.

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).

2021

In recent years, Quantum Computing witnessed massive improvements both in terms of resources availability and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn the scientific community’s interest since the late ’80s. In such a context, we pose our contribution. First, we introduce basic concepts related to quantum computations, and then we explain the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms. Finally, we gather, compare and analyze the current state-of-the-art concerning Quantum Perceptrons and Quantum Neural Networks implementations.

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.