The main goal of this master's thesis is to introduce Quantum Natural
Language Processing (QNLP) in a way understandable by both the NLP engineer and
the quantum computing practitioner. QNLP is a recent application of quantum
computing that aims at representing sentences' meaning as vectors encoded into
quantum computers. To achieve this, the distributional meaning of words is
extended by the compositional meaning of sentences (DisCoCat model) : the
vectors representing words' meanings are composed through the syntactic
structure of the sentence. This is done using an algorithm based on tensor
products. We see that this algorithm is inefficient on classical computers but
scales well using quantum circuits. After exposing the practical details of its
implementation, we go through three use-cases.

该硕士论文介绍了量子自然语言处理（QNLP）的实现细节，其中采用基于张量积的算法将表示单词含义的向量通过句子的句法结构进行组合，并应用于三种实际应用场景。

量子自然语言处理简介

A gentle introduction to Quantum Natural Language Processing

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a
compositional model of meaning for distributional semantics, in which each word
in a sentence has a meaning vector and the distributional meaning of the
sentence is a function of the tensor products of the word vectors. Abstractly
speaking, this function is the morphism corresponding to the grammatical
structure of the sentence in the category of finite dimensional vector spaces.
In this paper, we provide a concrete method for implementing this linear
meaning map, by constructing a corpus-based vector space for the type of
sentence. Our construction method is based on structured vector spaces whereby
meaning vectors of all sentences, regardless of their grammatical structure,
live in the same vector space. Our proposed sentence space is the tensor
product of two noun spaces, in which the basis vectors are pairs of words each
augmented with a grammatical role. This enables us to compare meanings of
sentences by simply taking the inner product of their vectors.

本文提供了一种用于实现分布式语义中语义合成模型的矢量空间的具体方法，实现方法基于结构化向量空间及张量积原理，将所有句子的语义矢量存在同一向量空间，并将提出的句子空间设置为两个名词空间的张量积，并通过它们的向量内积来比较句子的语义。

意义组合分布式模型的具体句子空间

Concrete Sentence Spaces for Compositional Distributional Models of  Meaning

We describe recent work of Klyachko, Totaro, Knutson, and Tao, that
characterizes eigenvalues of sums of Hermitian matrices, and decomposition of
tensor products of representations of $GL_n(\mathbb{C})$. We explain related
applications to invariant factors of products of matrices, intersections in
Grassmann varieties, and singular values of sums and products of arbitrary
matrices.

该论文讨论了 Klyachko、Totaro、Knutson 和 Tao 的最近研究，该研究表征了 Hermitian 矩阵之和的特征值，以及 GL_n（C）的表示的张量积的分解，进而应用到矩阵积的不变因子、Grassmann 空间中的交点问题以及任意矩阵之和与积的奇异值。