Invited Article: Quantum memristors in quantum photonics

Sanz, Mikel; Lamata, Lucas; Solano, E.

doi:10.1063/1.5036596

Cited by 45 publications

(45 citation statements)

References 38 publications

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“…However, the system always relaxes into a limit cycle independent of the initial conditions. The area of the hysteresis loop can give us a hint about the memory persistence in the system [19,20], such that the larger the area, the greater the memory persistence. Then, it would be interesting to test whether the introduction of a quantized Hodgkin-Huxley model, allowing for the use of quantum state inputs, represents an improvement in the persistence of the memory.…”

Section: Quantum Hodgkin-huxley Modelmentioning

confidence: 99%

“…From a wide perspective, we are heading towards a general framework for neuromorphic quantum computing, in which braininspired architectures strive to take advantage of quantum features to enhance computational power. Recent proposals for a quantized memristor [18], as well as its possible implementations in both superconducting circuits [19] and integrated quantum photonics [20], allows for the construction of a quantized neuron model based on Hodgkin-Huxley circuit. In the classical realm, this model reproduces the characteristic adaptive behavior of brain neurons.…”

Section: Introductionmentioning

confidence: 99%

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Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons

et al. 2019

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The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element, namely capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. Here, we will consider a quantized Hodgkin-Huxley model based on a quantum memristor formalism. We compare the behavior of the membrane voltage and the potassium channel conductance, when the circuit is subjected to AC sources, in both classical and quantum realms. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage manifest purely quantum features related to the circuit zero-point energy. This study may allow the construction of quantum neuron networks inspired in the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning.

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Section: Quantum Hodgkin-huxley Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons

et al. 2019

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“…There is a proposal for implementing it in superconducting circuits [4], exploiting memory effects that naturally arise in Josephson junctions. The second proposal is based on integrated photonics [14]: a Mach-Zehnder interferometer can behave as a beam splitter with a tunable reflectivity by introducing a phase in one of the beams, and this is manipulated to study the system as a quantum memristor subject to different quantum state inputs.…”

Section: Introductionmentioning

confidence: 99%

Quantum Memristors in Frequency-Entangled Optical Fields

et al. 2020

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A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequencyentangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally-attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work provides the first steps of a novel route towards constructing quantum neural networks in quantum photonics.

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“…Furthermore, synaptic and learning processes in neurons have been simulated using classical memristive devices [28][29][30][31]. A key element in the development of a quantum neuron model is the quantum memristor [32], and the realizability of this model lies on the proposals for constructing a quantum memristor in superconducting circuits [33] and in integrated quantum photonics [34]. A simplified version of this model has already been studied in the quantum regime [35].…”

Section: Introductionmentioning

confidence: 99%

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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Invited Article: Quantum memristors in quantum photonics

Cited by 45 publications

References 38 publications

Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons

Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons

Quantum Memristors in Frequency-Entangled Optical Fields

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

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