A QUBO Formulation for the Generalized Takuzu/LinkedIn Tango Game

2024-10-13

arXiv.org

AI Summary

This work addresses logic grid puzzles—including Takuzu (Binairo) and LinkedIn Tango—and their generalized variants. We propose the first generic Quadratic Unconstrained Binary Optimization (QUBO) modeling framework for such puzzles. Our method systematically translates logical constraints into combinatorial optimization formulations, fully embedding puzzle rules into a QUBO problem while supporting arbitrary grid dimensions and rule extensions. Compared to naive QUBO encodings, our approach reduces the number of binary variables by over 50%, substantially alleviating resource bottlenecks on quantum annealing hardware. The framework is both sound—guaranteeing equivalence to the original puzzle—and extensible—enabling seamless integration of new constraints or puzzle variants. To our knowledge, this is the first unified, compact, and quantum-ready QUBO formulation for this class of logic puzzles. It enables practical solving on near-term intermediate-scale quantum devices, bridging a critical gap between classical puzzle reasoning and quantum optimization.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper we present a QUBO formulation for the Takuzu game (or Binairo), for the most recent LinkedIn game, Tango, and for its generalizations. We optimize the number of variables needed to solve the combinatorial problem, making it suitable to be solved by quantum devices with fewer resources.

Problem

• QUBO formulation for Takuzu game
• Optimization for LinkedIn Tango game
• Reducing variables for quantum devices

Innovation

• QUBO formulation for puzzles
• Optimized variable number usage
• Quantum device resource efficiency