Neural optimization for quantum architectures: graph embedding problems with Distance Encoder Networks

Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still a complicated task. One of the main challenges is to represent through qubits (i.e., the basic units of quantum information) the problems of interest. According to the specific technology underlying the quantum machine, it is necessary to implement a proper representation strategy, generally referred to as embedding. This paper introduces a neural-enhanced optimization framework to solve the constrained unit disk problem, which arises in the context of qubits positioning for neutral atoms-based quantum hardware. The proposed approach involves a modified autoencoder model, i.e., the Distances Encoder Network, and a custom loss, i.e., the Embedding Loss Function, respectively, to compute Euclidean distances and model the optimization constraints. The core idea behind this design relies on the capability of neural networks to approximate non-linear transformations to make the Distances Encoder Network learn the spatial transformation that maps initial non-feasible solutions of the constrained unit disk problem into feasible ones. The proposed approach outperforms classical solvers, given fixed comparable computation times, and paves the way to address other optimization problems through a similar strategy.