Optimisation challenge for superconducting adiabatic neural network implementing XOR and OR boolean functions

TL;DR

This work addresses the optimization of adiabatic superconducting neural networks built from Josephson cells to implement XOR and OR logic. It introduces a gradient-descent approach targeting the synapse slope angle $\tan{\alpha}$, deriving algebraic conditions at the inflection point to avoid full dynamical simulation. The authors demonstrate parameter tuning improves synaptic weights and output currents, and propose circuit-structure modifications (galvanic coupling) to mitigate signal loss, with successful XOR/OR realizations in a 3-neuron network. The findings suggest scalability to larger networks using local optimisation strategies and discuss experimental feasibility using existing Josephson junction technologies, highlighting potential for energy-efficient neuromorphic hardware and hybrid quantum-classical computing interfaces.

Abstract

In this article, we consider designs of simple analog artificial neural networks based on adiabatic Josephson cells with a sigmoid activation function. A new approach based on the gradient descent method is developed to adjust the circuit parameters, allowing efficient signal transmission between the network layers. The proposed solution is demonstrated on the example of the system implementing XOR and OR logical operations.

Figures (12)

• Figure 1: OpenAI's DALLE 3 prompt-generated image of a superconducting neural network simulating an XOR operation.
• Figure 2: Schematic representation of two coupled $S_c$-neurons (input -- in cyan box and output -- in navy blue box), connected through the inductive synapse (in the green box) and the coupler -- integrating part of the output neuron (in the light yellow box). Processing part of the
• Figure 3: Activation functions for the first (input) and second (output) neurons. The "red" curve corresponds to $i_{out1}$, the "blue" curve corresponds to $i_{out2}$. Parameters of the system: $l_{1,2}=0.2$, $l_{out1}=l_{out2}=1$, $l_{a1,a2}=l_{1,2}+1$, $l_{in}=1$, $l_{t1}=l_{t2}=0.1$, $l_{t3}=l_{t4}=1$, $l_{s1}+l_{s2}=1$, $l_{s1}-l_{s2}=0.9$.
• Figure 4: Synaptic weights without system parameters optimisation: (a) dependence of the output current from the synapse ($\Delta i_s = i_{s1} - i_{s2}$) as a function of the input current ($i_{in}$) and (b) calculations for the dependence of the slope angle $\alpha$ on $\Delta l_s = l_{s1} - l_{s2}$. Parameters of the system: $l_{1,2}=0.2$, $l_{out1}=l_{out2}=1$, $l_{a1,a2}=l_{1,2}+1$, $l_{in}=1$, $l_{t1}=l_{t2}=0.1$, $l_{t3}=l_{t4}=1$, $l_{s1}+l_{s2}=1$.
• Figure 5: Gradient descent trajectories for $\max\alpha$ maximisation for different initial parameters (shown by different colors), projected onto the plane $\{l_{in};l_{t1,t2}\}$.