论文标题
线性光量子计算的类别
The Category of Linear Optical Quantum Computing
论文作者
论文摘要
本说明回顾了由光子电路生成的计算模型，其中包括在单个时池和由理想化的无损耗梁拆分器和相位变速器给出的光子横穿的边缘。该电路模型被抽象为多模光子骨化矩阵上单位矩阵的对称单类类别的表示。提出了一种旨在帮助理解和开发光子算法的示意语言，它涵盖了该表示形式的类别属性。作为形式主义的演示，在单轨光子计算机上开发了玻色子采样方案以及Knill，Laflamme和Milburn的方案，并研究了基于平价的Qudit模型。
This note reviews the model of computation generated by photonic circuits, comprising edges that are traversed by photons in a single time-bin and vertices given by idealised lossless beam splitters and phase shifters. The circuit model is abstracted as a representation of the symmetric monoidal category of unitary matrices on the bosonic Fock space of multimode photons. A diagrammatic language, designed to aid with the understanding and development of photonic algorithms, is presented that encapsulates the category properties of this representation. As demonstrations of the formalism, the boson sampling scheme and the protocol of Knill, Laflamme and Milburn are developed on the single-rail photonic computer, and a parity-based model for the qudit is investigated.
