  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.
