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

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.

量子计算在有效探索解决方案空间和增强供应链和物流优化任务方面显示出巨大潜力。量子计算中的一个关键工具，称为离散量子行走，可用于构建量子电路和对包括格罗弗搜索在内的多种量子算法进行建模。虽然离散量子行走的优势通过数值证据变得显而易见，但缺乏一个统一的图论框架来让研究人员证明这些优势。为了弥补这一差距，该项目解决了以下问题：离散量子行走的行为如何由底层图的组合属性决定？这个问题的答案将有助于查明离散量子行走在其上表现出优势的图，并最终导致基于量子行走的算法的新构造。该项目的更广泛影响包括人工智能技术、生物医学研究、气候科学、优化、金融建模以及量子科学和技术领域多元化劳动力的培训等受量子启发的变革。该项目的技术目标是证明（或反驳）使用图论和代数研究离散量子行走中的某些现象。研究人员之前的工作揭示了离散量子行走的跃迁矩阵与各种组合结构的入射矩阵之间的谱关系。基于这些关系，该项目将 (1) 提供“光谱良好”的图表征，以实现所需的量子现象，例如高保真状态转移和均匀混合，(2) 在离散量子行走和连续量子之间建立联系游走，它们在物理上不同，但共享可转移的数学机制，并且（3）确定用于解决困难组合问题的离散量子游走方法的测试用例，从而评估其有效性。该项目的成果不仅将增进对量子行走的科学理解，还将通过将这些发现纳入未来的量子计算课程并让学生参与指导活动来丰富教育经验。该奖项反映了 NSF 的法定使命，经评估认为值得支持利用基金会的智力优势和更广泛的影响审查标准。