We discuss several mappings from well-known NP-hard problems to Quadratic Unconstrained Binary Optimisation problems which are treated incorrectly by Lucas. We provide counterexamples and correct the mappings. We also extend the body of QUBO formulations of NP-complete and NP-hard optimisation problems by discussing additional problems.

中文翻译：

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将 NP-hard 和 NP-complete 优化问题映射到二次无约束二元优化问题

我们讨论了从众所周知的 NP-hard 问题到 Lucas 错误处理的二次无约束二元优化问题的几种映射。我们提供反例并纠正映射。我们还通过讨论其他问题扩展了 NP 完全和 NP 难优化问题的 QUBO 公式的主体。