arXiv subjects

A. D. Correia

Publications and source records attributed to A. D. Correia.

3 recordsLinked to original sources

arXiv2022

Grover's Algorithm for Question Answering

Grover's algorithm, a well-know quantum search algorithm, allows one to find the correct item in a database, with quadratic speedup. In this paper we adapt Grover's algorithm to the problem of finding a correct answer to a natural language question in English, thus contributing to the growing field of Quantum Natural Language Processing. Using a grammar that can be interpreted as tensor contractions, each word is represented as a quantum state that serves as input to the quantum circuit. We here introduce a quantum measurement to contract the representations of words, resulting in the representation of larger text fragments. Using this framework, a representation for the question is found that contains all the possible answers in equal quantum superposition, and allows for the building of an oracle that can detect a correct answer, being agnostic to the specific question. Furthermore, we show that our construction can deal with certain types of ambiguous phrases by keeping the various different meanings in quantum superposition.

quant-ph↗

arXiv2021

Asymmetric games on networks: towards an Ising-model representation

We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in numerical simulations of repeated games on networks until convergence is reached. As a result, correlations between the choices of the players emerge. Our approach is to study these correlations with a generalized Ising model. Using the response strategy framework, we describe how the actions of the players can bring the network into a steady configuration, starting from an out-of-equilibrium one. We obtain these configurations using game-theoretical tools, and describe the results using Ising parameters. We exhaust the two-player case, giving a detailed account of all the equilibrium possibilities. Going to three players, we generalize the Ising model and compare the equilibrium solutions of three representative types of network. We find that players that are not directly linked retain a degree of correlation that is proportional to their initial correlation. We also find that the local network structure is the most relevant for small values of the magnetic field and the interaction strength of the Ising model. Finally, we conclude that certain parameters of the equilibrium states are network independent, which opens up the possibility of an analytical description of asymmetric games played on networks.

physics.soc-ph↗

arXiv2018

Nash Equilibria in the Response Strategy of Correlated Games

In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the correlations that influence the decisions of the players. The current theory for correlated games, however, enforces the players to obey the instructions from a third party or "correlation device" to reach equilibrium, but this cannot be achieved for all initial correlations. We extend here the existing framework of correlated games and find that there are other interesting and previously unknown Nash equilibria that make use of correlations to obtain the best payoff. This is achieved by allowing the players the freedom to follow or not to follow the suggestions of the correlation device. By assigning independent probabilities to follow every possible suggestion, the players engage in a response game that turns out to have a rich structure of Nash equilibria that goes beyond the correlated equilibrium and mixed-strategy solutions. We determine the Nash equilibria for all possible correlated Snowdrift games, which we find to be describable by Ising Models in thermal equilibrium. We believe that our approach paves the way to a study of correlations in games that uncovers the existence of interesting underlying interaction mechanisms, without compromising the independence of the players.

physics.soc-ph↗