Analog simulator of integro-differential equations with classical memristors

Barrios, G. Alvarado; Retamal, J. C.; Solano, E.

doi:10.1038/s41598-019-49204-y

Cited by 19 publications

(9 citation statements)

References 43 publications

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“…While this version accounted for the dynamics of the potassium channel solely, we consider the composite action of the potassium, sodium, and chloride channels, which represent the complete Hodgkin-Huxley model. This study is supported by previous works describing coupled memristor circuits [36][37][38][39], concerning parallely connected memristors.…”

Section: Introductionsupporting

confidence: 80%

Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials

Gonzalez-Raya

Solano

Sanz

2020

Quantum

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The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described employing multiple connected electric circuits containing capacitors, voltage sources, and conductances. These conductances depend on previous depolarizing membrane voltages, which can be identified with a memory resistive element called memristor. Inspired by the recent quantization of the memristor, a simplified Hodgkin-Huxley model including a single ion channel has been studied in the quantum regime. Here, we study the quantization of the complete Hodgkin-Huxley model, accounting for all three ion channels, and introduce a quantum source, together with an output waveguide as the connection to a subsequent neuron. Our system consists of two memristors and one resistor, describing potassium, sodium, and chloride ion channel conductances, respectively, and a capacitor to account for the axon's membrane capacitance. We study the behavior of both ion channel conductivities and the circuit voltage, and we compare the results with those of the single channel, for a given quantum state of the source. It is remarkable that, in opposition to the single-channel model, we are able to reproduce the voltage spike in an adiabatic regime. Arguing that the circuit voltage is a quantum variable, we find a purely quantum-mechanical contribution in the system voltage's second moment. This work represents a complete study of the Hodgkin-Huxley model in the quantum regime, establishing a recipe for constructing quantum neuron networks with quantum state inputs. This paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.

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Section: Introductionsupporting

confidence: 80%

Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials

Gonzalez-Raya

Solano

Sanz

2020

Quantum

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“…Compute the local gradient of the node memristor using Equation (16). end for for layer in hidden layers do for node in layer do Compute the local gradient of node memristor l in layer using Equation (17) In this model, memristors are used to emulate both the connections and the nodes of a MLP.…”

Section: Algorithm 2 Backpropagation For Multilayer Perceptronmentioning

confidence: 99%

“…Despite having been predicted in 1971 using this argument, it was not until 2008 that the existence of memristors was demonstrated at HP Labs [11], which led to a new boom in memristor-related research [12]. In particular, there have been proposals of how memristors could be used in Hebbian learning systems [13][14][15], in the simulation of fluid-like integro-differential equations [16], in the construction of digital quantum computers [17] and of how they could be used to implement non-volatile memories [18].…”

Section: Introductionmentioning

confidence: 99%

Perceptrons from memristors

et al. 2020

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Memristors, resistors with memory whose outputs depend on the history of their inputs, have been used with success in neuromorphic architectures, particularly as synapses and non-volatile memories. However, to the best of our knowledge, no model for a network in which both the synapses and the neurons are implemented using memristors has been proposed so far. In the present work we introduce models for single and multilayer perceptrons based exclusively on memristors. We adapt the delta rule to the memristor-based single-layer perceptron and the backpropagation algorithm to the memristor-based multilayer perceptron. Our results show that both perform as expected for perceptrons, including satisfying Minsky-Paperts theorem. As a consequence of the Universal Approximation Theorem, they also show that memristors are universal function approximators. By using memristors for both the neurons and the synapses, our models pave the way for novel memristor-based neural network architectures and algorithms. A neural network based on memristors could show advantages in terms of energy conservation and open up possibilities for other learning systems to be adapted to a memristor-based paradigm, both in the classical and quantum learning realms.

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“…Exploring novel approaches to improve the computational capacity and efficiency is a goal that humans have been continuously pursuing. Early computers are constructed mechanically [1] or electronically [2][3][4] on the principle of analog, aiming to perform mathematical operations. Despite the impressive success achieved in the fields of weather prediction, aerospace and nuclear industry, these machines faced significant obstacles of slow response and large size [5].…”

Section: Introductionmentioning

confidence: 99%

Optical Realization of Wave-Based Analog Computing with Metamaterials

et al. 2020

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Recently, the study of analog optical computing raised renewed interest due to its natural advantages of parallel, high speed and low energy consumption over conventional digital counterpart, particularly in applications of big data and high-throughput image processing. The emergence of metamaterials or metasurfaces in the last decades offered unprecedented opportunities to arbitrarily manipulate the light waves within subwavelength scale. Metamaterials and metasurfaces with freely controlled optical properties have accelerated the progress of wave-based analog computing and are emerging as a practical, easy-integration platform for optical analog computing. In this review, the recent progress of metamaterial-based spatial analog optical computing is briefly reviewed. We first survey the implementation of classical mathematical operations followed by two fundamental approaches (metasurface approach and Green’s function approach). Then, we discuss recent developments based on different physical mechanisms and the classical optical simulating of quantum algorithms are investigated, which may lead to a new way for high-efficiency signal processing by exploiting quantum behaviors. The challenges and future opportunities in the booming research field are discussed.

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Analog simulator of integro-differential equations with classical memristors

Cited by 19 publications

References 43 publications

Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials

Quantized Three-Ion-Channel Neuron Model for Neural Action Potentials

Perceptrons from memristors

Optical Realization of Wave-Based Analog Computing with Metamaterials

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