Dynamic Processes in a Superconducting Adiabatic Neuron with Non-Shunted Josephson Contacts

Abstract

We investigated the dynamic processes in a superconducting neuron based on Josephson contacts without resistive shunting (SC-neuron). Such a cell is a key element of perceptron-type neural networks that operate in both classical and quantum modes. The analysis of the obtained results allowed us to find the mode when the transfer characteristic of the element implements the “sigmoid” activation function. The numerical approach to the analysis of the equations of motion and the Monte Carlo method revealed the influence of inertia (capacitances), dissipation, and temperature on the dynamic characteristics of the neuron.

A superconducting adiabatic neuron in a quantum regime

“…Numerical analysis has shown that the activation functions for the quantum neuron, initialised in the basic states, takes a sigmoidal shape (black and red curves in Figure 3 ). This is in a good agreement with the classical regime of operation [ 46 ].…”

“…A single-junction superconducting interferometer with normalized inductance l , a Josephson junction without resistive shunting (JJ), an additional inductance l a , and an output inductance l out (see Figure 1b ) are the basis of the quantum neuron. This circuit has been presented before as a classic superconducting neuron for an adiabatic perceptron [ 42 , 46 ].…”

“…These coefficients were introduced in [ 46 ] when considering the classical mode of this system. Inductances are normalized to (2π I c /Φ 0 ), where I c is the critical current of the Josephson junction and Φ 0 is the magnetic flux quantum.…”

“…Note that for the classical regime the sigmoidal shape of the activation function is possible only when l < l * [ 46 ].…”

“…An important incentive for this work are the previously obtained results on classical adiabatic neurons with extremely small energy dissipation [ 42 – 45 ]. We especially note the demonstrated possibility of the adiabatic evolution of the state for a neuron in a multilayer perceptron with Josephson junctions without resistive shunting [ 46 ]. It is precisely such a heterostructure without resistive shunting that is used in the implementation of a quantum neuron based on a flux qubit.…”