发表机构
University of Science and Technology of China; University of Wisconsin-Madison（中国科学技术大学; 威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对共轭闭复值签名集的布尔Holant问题，证明了与实值情形相同的四条件二分法，并利用射影二元群框架、量子纠缠及绝对最大纠缠态分类解决归纳证明中的6元障碍。
AI 中文摘要
我们研究签名集在共轭下封闭的复值布尔Holant问题。这类集合自然出现在量子电路的经典强模拟的张量网络表达式中。我们证明了此类问题的一个复杂性二分法，并给出了显式的可判定性准则。这扩展了实值Holant问题的二分法，且具有相同的四个可判定性条件。我们的证明使用了Xia的射影二元群框架和量子纠缠理论。共轭闭包假设恰好使$k$-均匀性直接适用于Holant问题的分类，通过Holant小工具实现约化密度矩阵。我们还使用绝对最大纠缠态的分类来解决我们归纳证明\#P-困难性中的一个特定的$6$元障碍。
英文摘要
We study Boolean Holant problems with complex-valued signature sets closed under conjugation. Such sets arise naturally in tensor-network expressions for classical strong simulation of quantum circuits. We prove a complexity dichotomy for such problems with an explicit tractability criterion. This extends the dichotomy for real-valued Holant problems, with the same four tractability conditions. Our proofs use Xia's projective binary group framework and quantum entanglement theory. The conjugate closure assumption precisely makes $k$-uniformity, directly applicable to the classification of Holant problems, by realizing reduced density matrices via Holant gadgets. We also use the classification of absolutely maximally entangled states to resolve a particular $6$-ary obstruction in our inductive proof of the \#P-hardness.
Comments96 pages, 3 figures
