After the NP-hardness of computational problems such as 3SAT and MaxCut was established, a natural next step was to explore whether these problems remain hard to approximate. While the quantum extensions of some of these problems are known to be hard-indeed undecidable-their inapproximability remains largely unresolved. In this work, we introduce definitions for the quantum extensions of Label-Cover and Unique-Label-Cover. We show that these problems play a similarly crucial role in studying the inapproximability of quantum constraint satisfaction problems as they do in the classical setting.

翻译：在3SAT和MaxCut等计算问题的NP难性被确立后，一个自然的后续步骤是探究这些问题是否在近似求解时依然困难。尽管其中某些问题的量子扩展已被证明是困难的——实际上是不可判定的——但它们的不可近似性在很大程度上仍未得到解决。在本研究中，我们为Label-Cover和Unique-Label-Cover的量子扩展提出了定义。我们证明，这些问题在研究量子约束满足问题的不可近似性时，发挥着与经典设定中同样关键的作用。