论文标题
意思是更新密度矩阵
Meaning updating of density matrices
论文作者
论文摘要
自然语言含义的Discocat模型为给定的句子分配了含义：（i）单词的含义，以及（ii）其语法结构。最近引入的cycocirc模型将其扩展到由多个句子组成的文本。在Discocat中，所有含义都是固定的，而在cascirc中，每个句子更新单词的含义。在本文中，我们探讨了cyocirc的不同更新机制，如果在密度矩阵中编码的含义 - 与向量相比，它们具有多种优势。 我们的起点是两个非交通性更新机制，从Leifer和Spekkens借用量子基础研究。不幸的是，这些都不满足任何理想的代数属性，也不满足含义类别的内部。通过传递双密度矩阵，我们确实获得了优雅的内部图形更新机制。 我们还表明，（交换）蜘蛛可以作为Leifer-Spekkens更新机制的实例施放。量子基础引起了这种结果，因为它将作品与条件量子状态桥接了分类量子力学（CQM）。我们的工作还支持了对量子硬件（又称QNLP）的文本级自然语言处理的实施，以前已经确定了指数增强和二次加速的量子。
The DisCoCat model of natural language meaning assigns meaning to a sentence given: (i) the meanings of its words, and, (ii) its grammatical structure. The recently introduced DisCoCirc model extends this to text consisting of multiple sentences. While in DisCoCat all meanings are fixed, in DisCoCirc each sentence updates meanings of words. In this paper we explore different update mechanisms for DisCoCirc, in the case where meaning is encoded in density matrices---which come with several advantages as compared to vectors. Our starting point are two non-commutative update mechanisms, borrowing one from quantum foundations research, from Leifer and Spekkens. Unfortunately, neither of these satisfies any desirable algebraic properties, nor are internal to the meaning category. By passing to double density matrices we do get an elegant internal diagrammatic update mechanism. We also show that (commutative) spiders can be cast as an instance of the Leifer-Spekkens update mechanism. This result is of interest to quantum foundations, as it bridges the work in Categorical Quantum Mechanics (CQM) with that on conditional quantum states. Our work also underpins implementation of text-level natural language processing on quantum hardware (a.k.a. QNLP), for which exponential space-gain and quadratic speed-up have previously been identified.
