CRII: FET: Quantum Advantages through Discrete Quantum Walks

CRII：FET：离散量子行走的量子优势

• 批准号: 2348399
• 负责人: Hanmeng Zhan
• 金额: $ 17.44万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-04-01 至 2026-03-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2348399&HistoricalAwards=false
• 关键词: CRII; FET; Quantum; Advantages; through; CRII; FET; Quantum; Advantages; through

Quantum computing has shown great potential in efficiently exploring solution spaces and enhancing optimization tasks in supply chain and logistics. A key tool in quantum computing, known as discrete quantum walks, can be used to build quantum circuits and model a number of quantum algorithms including Grover's search. While advantages of discrete quantum walks become clear through numerical evidence, a unified, graph-theoretical framework that allows researchers to prove these advantages is missing. To bridge the gap, this project addresses the following question: how is the behavior of a discrete quantum walk determined by the combinatorial properties of the underlying graph? Answers to this question will help pinpoint graphs on which discrete quantum walks exhibit advantages, and ultimately lead to new constructions of quantum-walk-based algorithms. Broader impacts of this project include quantum-inspired transformations in AI technology, biomedical research, climate science, optimization, financial modelling, and training of a diverse workforce in quantum science and technology.The technical objective of this project is to prove (or disprove) certain phenomena in discrete quantum walks using graph theory and algebra. Prior work by the investigator has revealed spectral relations between the transition matrix of a discrete quantum walk and the incidence matrices of various combinatorial structures. Built upon these relations, this project will (1) offer characterizations of graphs that are "spectrally nice" to enable desired quantum phenomena, such as high-fidelity state transfer and uniform mixing, (2) establish connections between discrete quantum walks and continuous quantum walks, which are physically different but share transferable mathematical machinery, and (3) identify test cases for discrete-quantum-walk approaches to hard combinatorial problems, thereby assessing their effectiveness. Outcomes of this project will not only advance scientific understanding of quantum walks, but also enrich educational experience by incorporating these findings into future quantum computing courses and engaging students in mentoring activities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

量子计算在有效地探索解决方案空间并增强供应链和物流中的优化任务方面显示出很大的潜力。量子计算中的关键工具，称为离散量子步行，可用于构建量子电路并建模许多量子算法，包括Grover的搜索。尽管通过数值证据明确了离散量子步行的优势，但统一的图形理论框架使研究人员无法证明这些优势是缺失的。为了弥合差距，该项目解决了以下问题：如何由基础图的组合属性确定离散量子步行的行为？这个问题的答案将有助于查明图形在哪些离散量子步行方面具有优势，并最终导致基于量子步行的算法的新结构。该项目的更广泛影响包括AI技术，生物医学研究，气候科学，优化，财务建模以及对量子科学和技术多元化劳动力的培训的量子启发的转型。该项目的技术目标是证明（或使用图形理论和Algebra）在离散量子步行中（或反对）某些现象。研究人员的先前工作揭示了离散量子步行的过渡矩阵与各种组合结构的发病率矩阵之间的光谱关系。基于这些关系，该项目将（1）提供图形的特征​​，这些图表“光谱很好”以实现所需的量子现象，例如高保真状态转移和均匀的混合，（2）在离散的量子步行和连续的量子步行之间建立连接，这些量子步行和连续的量子步行之间是在物理上具有不同但可以共享的可转移的验证案例的方法，以实现易于转移的方法，以及（3）符合智能的机制，以及（3）既定的智能机制，以及（3）评估其有效性。该项目的成果不仅将对量子步行进行科学理解，而且还可以通过将这些发现纳入未来的量子计算课程中，并吸引学生参与指导活动。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力和更广泛影响的评估来通过评估来支持的，这是值得的。