A QUBO Formulation for the Generalized LinkedIn Queens and Takuzu/Tango Game

TL;DR

This paper develops a QUBO formulation to solve various combinatorial puzzles, including generalized versions of the N-queens, Takuzu, and Tango games, aiming for quantum hardware applications.

Contribution

It introduces a unified QUBO approach for multiple puzzles and optimizes it for quantum annealing and QAOA, also proposing new problem types with formulations.

Findings

QUBO formulations enable solving complex puzzles on quantum hardware.

Optimized formulations reduce variables and interactions, improving hardware applicability.

New problem types with corresponding QUBO formulations are introduced.

Abstract

In this paper, we present a QUBO formulation designed to solve a series of generalisations of the LinkedIn queens game, a version of the N-queens problem, for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for its generalizations. We adapt this formulation for several particular cases of the problem, as Tents \& Trees, by trying to optimise the number of variables and interactions, improving the possibility of applying it on quantum hardware by means of Quantum Annealing or the Quantum Approximated Optimization Algorithm (QAOA). We also present two new types of problems, the Coloured Chess Piece Problem and the Max Chess Pieces Problem, with their corresponding QUBO formulations.