The paper reviews QUDO, T-QUDO and HOBO formulations, provides explicit encodings between them, discusses limitations, and gives examples for knapsack, TSP and games including N-Queens and Peg Solitaire.
A QUBO Formulation for the Generalized LinkedIn Queens and Takuzu/Tango Game
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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.
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cs.ET 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Introduction to QUDO, Tensor QUDO and HOBO formulations: Qudits, Equivalences, Knapsack Problem, Traveling Salesman Problem and Combinatorial Games
The paper reviews QUDO, T-QUDO and HOBO formulations, provides explicit encodings between them, discusses limitations, and gives examples for knapsack, TSP and games including N-Queens and Peg Solitaire.