Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons
This work may enable the construction of quantum neuron networks for brain-inspired computing and neuromorphic quantum architectures, though it is incremental as it adapts a classical model to quantum formalism.
The authors tackled the problem of modeling neural behavior in quantum systems by developing a quantized version of the Hodgkin-Huxley model, focusing on the potassium ion channel as a quantum memristor, and found that numerical simulations revealed quantum features like zero-point energy effects in voltage moments.
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.