Quantized Hodgkin-Huxley Model for Quantum Neurons

The Hodgkin-Huxley model describes the conduction of the nervous impulse through the axon, whose membrane's electric response can be described by 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, the Hodgkin-Huxley model has been studied in the quantum regime. The circuit obtained in this model is proposed as the building block for the construction of quantum neurons networks which can process quantum information. Hence, we study two such circuits connected in series, coupled to a quantized source. Since the main quantum contribution on these systems comes from the second moment of the voltage, we study correlations such as degree of coherence, between voltage and conductance in both circuits, proving they are quantum variables. This study paves the way for advances in hardware-based neuromorphic quantum computing, as well as quantum machine learning, which might be more efficient resource-wise.