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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. 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.

A quantum memristor is a resistive passive circuit element with memory engineered in a given quantum platform. It can be represented by a quantum system coupled to a dissipative environment, in which a system-bath coupling is mediated through a weak measurement scheme and classical feedback on the system. In quantum photonics, such a device can be designed from a beam splitter with tunable reflectivity, which is modified depending on the results of measurements in one of the outgoing beams. Here, we show that a similar implementation can be achieved with frequencyentangled optical fields and a frequency mixer that, working similarly to a beam splitter, produces state superpositions. We show that the characteristic hysteretic behavior of memristors can be reproduced when analyzing the response of the system with respect to the control, for different experimentally-attainable states. Since memory effects in memristors can be exploited for classical and neuromorphic computation, the results presented in this work provides the first steps of a novel route towards constructing quantum neural networks in quantum photonics.

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Open-air microwave quantum communication and metrology protocols must be able to transfer quantum resources from a cryostat, where they are created, to an environment dominated by thermal noise. Indeed, the states carrying such quantum resources are generated in a cryostat characterized by a temperature Tin≃50 mK and an intrinsic impedance Zin=50Ω. Then, an antenna-like device is required to transfer them with minimal losses into open air, characterized by an intrinsic impedance of Zout=377Ω and a temperature Tout≃300 K. This device accomplishes a smooth impedance matching between the cryostat and the open air. Here, we study the transmission of two-mode squeezed thermal states, developing a technique to design the optimal shape of a coplanar antenna to preserve the entanglement. Based on a numerical optimization procedure, we find the optimal shape of the impedance, and we propose a functional ansatz to qualitatively describe this shape. Additionally, this study reveals that the reflectivity of the antenna is very sensitive to this shape, so that small changes dramatically affect the outcoming entanglement, which could have been a limitation in previous experiments employing commercial antennae. This work is relevant in the fields of microwave quantum sensing and quantum metrology with special application to the development of the quantum radar, as well as any open-air microwave quantum communication protocol.