量子态关于信道的相干及其在Grover搜索算法中的应用

量子相干源于叠加原理，是量子世界区别于经典世界的根本特征之一。量子信道是量子信息理论中的基本概念，在量子技术的实践中扮演重要角色。从量子信道的角度研究量子态的量子相干是将量子相干框架完备化的关键。同时，这也可以为刻画量子信道的相干、退相干能力提供一种新思路。此外，量子相干是实现量子计算的重要资源，克服噪声诱导的退相干是量子计算的核心问题，因此有必要深入探究量子相干在量子算法中的演化及其对算法效率的影响。本项目以量子态关于量子信道的相干为研究对象，旨在利用投影、等距嵌入等手段将量子态关于量子信道的相干的已有结果推广到一般情形，给出合理的相干度量；基于该度量量化量子信道的相干、退相干能力；探究量子态关于量子信道的相干在带噪声的Grover搜索算法中的动力学行为，并利用量子相干的资源理论分析该算法的量子优势。

Quantum coherence, which arises from the superposition principle, is one of the fundamental characteristics which differentiate quantum realm form the classical world. Quantum channel is a basic concept in quantum information theory which plays an important role in the practices of quantum technologies. In order to complete the framework of quantum coherence, it is necessary to consider the quantum coherence of quantum states relative to quantum channels. At the same time, this also provides a new way to characterize the cohering and decohering power of quantum channels. Furthermore, quantum coherence is an important resource to realize quantum computation, and it is the core problem of quantum computation to overcome the decoherence induced by noise. In this sense, it is necessary to explore the evolution of quantum coherence in quantum algorithm and its influence on algorithm efficiency in depth and detail. In this project, we aim to extend the existing results for quantum coherence of quantum states relative to a quantum channels to the general case by means of projection, isometric embedding and so on, to provide quantifications of the cohering and decohering power of quantum channel, to explore the dynamics of quantum coherence of quantum states with respect to quantum channels in noisy Grover’s search algorithm, and to analyze the quantum advantage of quantum algorithms by the resource theory of quantum coherence.