Quantum machine learning and linear algebra algorithms from spectral graph theory

谱图理论中的量子机器学习和线性代数算法

• 批准号: 1956604
• 金额: --
• 依托单位: University College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1956604
• 关键词: Quantum; machine; learning; linear; algebra

The problem of recognizing hidden structures in data is a fundamental one in a vast range of fields. Over the last two decades information technology has began to intensively rely on it. One of the main reasons is the increasing amount of data that is becoming available. In order to keep the pace with the amount of data we need to analyse, more efficient methods need to be found. The idea of quantum machine learning is to use the inherent properties of quantum mechanics to improve or speedup the process of algorithmic learning. Even though a quantum computer is not expected to solve NP-complete problems in polynomial time, it can non-trivially speedup classical algorithms for NP-complete problems. Many machine learning problems, as for example k-nearest-neighbour clustering, fall in the worst case scenario into this category. Therefore the hope is that these problems can obtain a non-trivial speed up in the quantum setting. In this project we specifically want to consider possible new ways of utilising insights from spectral graph theory in the area of quantum machine learning to design algorithms that can outperform their classical counterparts and potentially demonstrate 'supremacy' of quantum technologies.

识别数据中的隐藏结构是一个基础性的问题。在过去的二十年里，信息技术开始强烈地依赖于它，其中一个主要原因是越来越多的数据变得可用。为了跟上我们需要分析的数据量的步伐，需要找到更有效的方法。量子机器学习的思想是利用量子力学的固有特性来改进或加速算法学习的过程。尽管量子计算机不能在多项式时间内解决NP完全问题，但它可以大大加速NP完全问题的经典算法。许多机器学习问题，例如k-最近邻聚类，在最坏的情况下属于这一类。因此，希望这些问题可以在量子环境中获得非平凡的加速。在这个项目中，我们特别想考虑可能的新方法，利用量子机器学习领域的谱图理论的见解来设计算法，这些算法可以超越经典算法，并可能证明量子技术的“至高无上”。