Quantum Information-Constrained Optimal Transport

这项研究将与密歇根大学的Sandeep Pradhan Sadanandarao教授合作进行。它旨在开发一种称为量子信息约束最优传输的新理论，该理论通过利用麦克马斯特团队在机器学习方面的专业知识以及国际合作者在量子信息理论和量子场论方面的专业知识，将量子率失真理论和量子传输理论统一起来。这一新理论将揭示量子信息科学新兴领域的一系列问题，这些问题可以被建模为通过比特管道在源和目的地之间传输。特别是，它将为设计具有数字接口的量子机器学习系统提供架构原则。每当人们试图压缩或传输由量子机器学习算法提取的特征图时，就会出现这样的系统。传统的方法是设计数字部分（即，量子压缩和量子通信）和模拟部分（即，量子机器学习）的这种系统分开。因此，由于数字部分和模拟部分之间的失配，集成系统经常遭受显著的性能下降。在量子信息约束的最优输运框架中，这两部分从一开始就被联合考虑，从而可以相干地生活在所得到的系统中。该研究还提供了一种通过量子信息处理增强机器学习应用的系统方法，从而加快了从经典机器学习到量子机器学习的过渡。它将加强加拿大在信息理论、机器学习和量子物理研究方面的领导地位，并为这些社区之间的思想交流提供更多激励。通过该项目培训的HQP将发展跨多个学科的扎实技术技能，对信息科学和技术的广泛观点，以及与他人交流见解的能力。他们将有能力站在量子革命的最前沿。

The proposed research will be conducted through the collaboration with Prof. Sandeep Pradhan Sadanandarao from the University of Michigan. It aims to develop a new theory termed quantum information-constrained optimal transport, which unifies quantum rate-distortion theory and quantum transport theory, by leveraging the McMaster team's expertise on machine learning and the international collaborator's expertise on quantum information theory and quantum field theory. This new theory will shed light on a host of problems in the emerging field of quantum information science that can be modelled as transportation between source and destination through a bit pipeline. In particular, it will provide architectural principles for designing quantum machine learning systems with a digital interface. Such systems arise whenever one attempts to compress or transmit feature maps extracted by quantum machine learning algorithms. The conventional approach is to design the digital part (i.e., quantum compression and quantum communication) and the analog part (i.e., quantum machine learning) of such systems separately. As a consequence, the integrated system often suffers from significant performance degradation due to the mismatch between the digital part and the analog part. In the framework of quantum information-constrained optimal transport, these two parts are jointly considered from the very beginning, thus can live coherently in the resulting system. The proposed research also offers a systematic approach to empowering machine learning applications via quantum information processing, thus expedites the transition from classical machine learning to quantum machine learning. It will strengthen Canada's leadership in information theory, machine learning, and quantum physics research and provide more incentives for the exchange of ideas between these communities. The HQP trained through this project will develop solid technical skills across multiple disciplines, broad perspectives on information science and technology, and the ability to communicate their insights to others. They will be well equipped to stay at the forefront of the quantum revolution.