Word embedding is a fundamental technology in natural language processing. It
is often exploited for tasks using sets of words, although standard methods for
representing word sets and set operations remain limited. If we can leverage
the advantage of word embedding for such set operations, we can calculate
sentence similarity and find words that effectively share a concept with a
given word set in a straightforward way. In this study, we formulate
representations of sets and set operations in a pre-trained word embedding
space. Inspired by \textit{quantum logic}, we propose a novel formulation of
set operations using subspaces in a pre-trained word embedding space. Based on
our definitions, we propose two metrics based on the degree to which a word
belongs to a set and the similarity between embedding two sets. Our experiments
with Text Concept Set Retrieval and Semantic Textual Similarity tasks
demonstrated the effectiveness of our proposed method.

本研究提出了一种利用预训练词向量空间中的子空间进行集合运算的新方法，并在 Text Concept Set Retrieval 和 Semantic Textual Similarity 任务中进行了实验证明了该方法的有效性。

基于子空间的预训练词嵌入空间集合运算

Subspace-based Set Operations on a Pre-trained Word Embedding Space

Linear optics underpins tests of fundamental quantum mechanics and computer
science, as well as quantum technologies. Here we experimentally demonstrate
the longstanding goal of a single reprogrammable optical circuit that is
sufficient to implement all possible linear optical protocols up to the size of
that circuit. Our six-mode universal system consists of a cascade of 15
Mach-Zehnder interferometers with 30 thermo-optic phase shifters integrated
into a single photonic chip that is electrically and optically interfaced for
arbitrary setting of all phase shifters, input of up to six photons and their
measurement with a 12 single-photon detector system. We programmed this system
to implement heralded quantum logic and entangling gates, boson sampling with
verification tests, and six-dimensional complex Hadamards. We implemented 100
Haar random unitaries with average fidelity 0.999 $\pm$ 0.001. Our system is
capable of switching between these and any other linear optical protocol in
seconds. These results point the way to applications across fundamental science
and quantum technologies.

通过实验展示了使用一个可编程的光学电路实现所有可能的光学协议的方法，并演示了能够执行量子逻辑和纠缠门的六模通用光学系统，可以实现 Haar 随机幺正矩阵，为量子科技带来了应用前景。

通用线性光学

Universal Linear Optics

This invited chapter in the Handbook of Quantum Logic and Quantum Structures
consists of two parts: 1. A substantially updated version of quant-ph/0402130
by the same authors, which initiated the area of categorical quantum mechanics,
but had not yet been published in full length; 2. An overview of the progress
which has been made since then in this area.

本文主要包括两部分内容，第一部分是 AB 两位作者的 quant-ph/0402130 论文的更新版本，该论文开创了范畴量子力学领域，但是尚未完整出版；第二部分则概述了这一领域自那时以来所取得的进展情况。