Quantum Memristors with Superconducting Circuits

Salmilehto, Juha; Deppe, Frank; Ventra, Massimiliano Di; Sanz, Mikel; Solano, E.

doi:10.1038/srep42044

Cited by 64 publications

(72 citation statements)

References 30 publications

(97 reference statements)

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“…Thus, a memristor that undergoes a periodic control signal will display a hysteresis loop when plotting the response versus the control signal (current vs voltage). The slope of this curve is identified with the resistance of the device, and the area under it is associated with memory effects [33].…”

Section: B Memristormentioning

confidence: 99%

“…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%

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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: B Memristormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Gonzalez-Raya

Solano

Sanz

2020

Quantum

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“…There are however interesting proposals for building QNN components in hardware. [210][211][212][213]…”

Section: Quantum Neural Network-quantum Brains?mentioning

confidence: 99%

Can Biological Quantum Networks Solve NP‐Hard Problems?

Wendin

2019

Adv Quantum Tech

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There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines, let alone ordinary classical computers. During the last decades the question has therefore been raised whether it is needed to consider quantum effects to explain the imagined cognitive power of a conscious mind. Not surprisingly, the conclusion is that quantum‐enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence signaling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. The conclusion is that biological quantum networks can only approximately solve small instances of nonpolynomial (NP)‐hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to solve NP‐hard problems approximately. In the end it is a question of precision—Nature is approximate.

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“…Specifically, in a SQUID the logical "0" and "1" usually correspond to zero and a single flux quantum in the loop, respectively. More recently, other superconducting tunnel junction-based memory elements were suggested [31][32][33][34][35]. A memory based on a thermally-biased inductive SQUID could take advantage of the clear hysteretic behavior of the temperature of the cold electrode for proper values of the external flux.…”

Section: Thermal Modelmentioning

confidence: 99%

Hysteretic Superconducting Heat-Flux Quantum Modulator

et al. 2017

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We discuss heat transport in a thermally-biased SQUID in the presence of an external magnetic flux, when a non-negligible inductance of the SQUID ring is taken into account. A properly sweeping driving flux causes the thermal current to modulate and behave hysteretically. The response of this device is analysed as a function of both the hysteresis parameter and degree of asymmetry of the SQUID, highlighting the parameter range over which hysteretic behavior is observable. Markedly, also the temperature of the SQUID shows hysteretic evolution, with sharp transitions characterized by temperature jumps up to, e.g., ∼ 0.02 K for a realistic Al-based setup. In view of these results, the proposed device can effectively find application as a temperature-based superconducting memory element, working even at GHz frequencies by suitably choosing the superconductor on which the device is based.

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Quantum Memristors with Superconducting Circuits

Cited by 64 publications

References 30 publications

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

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

Can Biological Quantum Networks Solve NP‐Hard Problems?

Hysteretic Superconducting Heat-Flux Quantum Modulator

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