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的潜力。量子计算中的一个关键工具，被称为离散量子行走，可以用来构建量子电路和模拟包括Grover搜索在内的许多量子算法。虽然离散量子行走的优势通过数值证据变得清晰，但缺乏一个统一的图论框架，使研究人员能够证明这些优势。为了弥合这一差距，该项目解决了以下问题：离散量子行走的行为是如何由底层图的组合性质决定的？对这个问题的回答将有助于精确定位离散量子行走表现出优势的图形，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、金融建模以及培训量子科学和技术领域的多样化劳动力。该项目的技术目标是使用图论和代数证明（或反驳）离散量子行走中的某些现象。研究人员先前的工作揭示了离散量子行走的转移矩阵与各种组合结构的关联矩阵之间的光谱关系。建立在这些关系的基础上，该项目将（1）提供“光谱上很好”的图形的特征，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）建立离散量子行走和连续量子行走之间的联系，这在物理上是不同的，但共享可转移的数学机制，以及（3）识别离散量子行走方法对困难组合问题的测试案例，从而评估它们的有效性。该项目的成果不仅将促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，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。