Using Differential Evolution to avoid local minima in Variational Quantum Algorithms.

Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing in diverse fields. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them from scaling efficiently. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of these problems. To this end, we propose to apply the Differential Evolution (DE) algorithm to VQAs optimizations. Our hypothesis is that DE is resilient to vanishing gradients and local minima for two main reasons: (1) it does not depend on gradients, and (2) its mutation and recombination schemes allow DE to continue evolving even in these cases. To demonstrate the performance of our approach, first, we use a robust local minima problem to compare state-of-the-art local optimizers (SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum Eigensolver algorithm. Our results show that DE always outperforms local optimizers. In particular, in exact simulations of a 1D Ising chain with 14 qubits, DE achieves the ground state with a 100% success rate, while local optimizers only exhibit around 40%. We also show that combining DE with local optimizers increases the accuracy of the energy estimation once avoiding local minima. Finally, we demonstrate how our results can be extended to more complex problems by studying DE performance in a 1D Hubbard model.

Incorporating social opinion in the evolution of an epidemic spread.

The evolution of the COVID19 pandemic worldwide has shown that the most common and effective strategy to control it used worldwide involve imposing mobility constrains to the population. A determinant factor in the success of such policies is the cooperation of the population involved but this is something, at least, difficult to measure. In this manuscript, we propose a method to incorporate in epidemic models empirical data accounting for the society predisposition to cooperate with the mobility restriction policies.

Urbanity and the dynamics of language shift in Galicia.

Sociolinguistic phenomena often involve interactions across different scales and result in social and linguistic changes that can be tracked over time. Here, we focus on the dynamics of language shift in Galicia, a bilingual community in northwest Spain. Using historical data on Galician and Spanish speakers, we show that the rate at which shift dynamics unfold correlates inversely with the internal complexity of a region (approximated by the proportion of urban area). Less complex areas converge faster to steady states, while more complex ones sustain transitory dynamics longer. We further explore the contextual relevance of each region within the network of regions that constitute Galicia. The network is observed to sustain or reverse the dynamic rates. This model can introduce a competition between the internal complexity of a region and its contextual relevance in the network. Harnessing these sociodynamic features may prove useful in policy making to limit conflicts.