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

TL;DR

This paper introduces a quantum version of the Hodgkin-Huxley neuron model using a quantum memristor, demonstrating quantum effects in neuron-like circuits and exploring potential for quantum neural networks and neuromorphic quantum computing.

Contribution

It presents a quantized Hodgkin-Huxley model with a quantum memristor, analyzing its behavior and potential implementation in superconducting circuits for quantum neural networks.

Findings

Quantum features in voltage moments related to zero-point energy

Memristor conductance adapts to signal history in quantum regime

Potential implementation as superconducting quantum circuits

Abstract

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. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf SQUID in superconducting circuits. 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.