Dynamics of Coupled Hodgkin-Huxley Quantum Neurons

The Hodgkin-Huxley model describes the conduction of nervous impulses, realized by flows of different ionic species through the axon’s membrane, through a circuit featuring ionic conductances that depend on previous depolarizing voltages. This circuit, projected in the quantum realm [1,2], consists of a capacitor and a quantum memristor, that describe the axon membrane’s charging capacity and voltage-dependent memory response, respectively. We consider the connection of two such circuits in parallel, subjected to a quantized input source as a resonator capacitively coupled to the circuit [2], and study the dynamical system and the quantum correlations that arise between the two circuits. Since the main quantum contribution on these systems comes from the second moment of the voltage [1], we will investigate correlations such as degree of coherence, between voltage and conductance in both circuits, proving that these are quantum variables. This study paves the way for hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.

[1] T. Gonzalez-Raya, X. -H. Cheng, I. L. Egusquiza, X. Chen, M. Sanz, and E. Solano, Phys. Rev. Appl. 12, 014037 (2019).
[2] T. Gonzalez-Raya, E. Solano, and M. Sanz, Quantum 4, 224 (2020).