CAREER: Complexity Theory of Quantum States: A Novel Approach for Characterizing Quantum Computer Science

职业：量子态复杂性理论：表征量子计算机科学的新方法

• 批准号: 2339116
• 负责人: Nai-Hui Chia
• 金额: $ 78.82万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-05-01 至 2029-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2339116&HistoricalAwards=false
• 关键词: CAREER; Complexity; Theory; Quantum; States

Quantum computing can help solve some of the most complex problems in physics, chemistry, material design, optimization, and machine learning. Quantum complexity theory plays a crucial role in guiding the advancement of quantum computing. Nowadays, the study of quantum computing and quantum physics leads to many new computational tasks for dealing with quantum information. The theoretical framework in standard complexity theory might be insufficient to guide the investigation of these new problems. This award will provide a novel theoretical framework to steer the development of fast quantum algorithms for various new problems in quantum physics and computer science, and construct more secure quantum cryptography. Beyond technology, the award will support the (i) development of new quantum computing courses for science and engineering students that will be shared with nearby Hispanic-serving institutions in Houston, (ii) mentoring of students from underrepresented groups through the Research Emerging Scholars Program and the Quantum Research Experiences for Undergraduates Program, and (iii) institution of a Hybrid Quantum Computing Seminar to deepen the engagement with internal and external stakeholders in the quantum computing community.Quantum computing introduces many well-motivated computational tasks that ask to identify specific properties of input quantum states. For example, state tomography asks to learn the classical description of the input quantum states, and the security of quantum cryptography relies on the hardness of extracting information from quantum messages. However, the standard complexity theory for problems with classical inputs and outputs is inadequate for identifying the computational complexity of these new computational tasks. Therefore, this award seeks to advance the following three thrusts: (i) develop the complexity theory for problems that ask to identify specific properties of input quantum states, (ii) identify the security of quantum cryptographic primitives through the new complexity theory, and (iii) use the framework to characterize the computational hardness of variants of problems with quantum inputs.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.

量子计算可以帮助解决物理、化学、材料设计、优化和机器学习中一些最复杂的问题。量子复杂性理论在指导量子计算的发展中起着至关重要的作用。目前，量子计算和量子物理的研究导致了许多新的计算任务来处理量子信息。标准复杂性理论的理论框架可能不足以指导对这些新问题的研究。该奖项将提供一个新颖的理论框架，以指导量子物理和计算机科学中各种新问题的快速量子算法的发展，并构建更安全的量子密码学。除了技术之外，该奖项还将支持（i）为科学和工程专业的学生开发新的量子计算课程，这些课程将与休斯顿附近的西班牙裔服务机构共享，（ii）通过研究新兴学者计划和本科生量子研究经验计划指导来自代表性不足群体的学生，以及（iii）举办混合量子计算研讨会，加深与量子计算界内部和外部利益相关者的接触。量子计算引入了许多积极的计算任务，要求识别输入量子态的特定属性。例如，状态层析术要求学习输入量子态的经典描述，而量子密码术的安全性依赖于从量子信息中提取信息的难度。然而，经典的输入和输出问题的标准复杂性理论是不足以识别这些新的计算任务的计算复杂性。因此，该奖项旨在推进以下三个方面：（i）为要求识别输入量子态的特定属性的问题发展复杂性理论，（ii）通过新的复杂性理论识别量子密码原语的安全性，以及（iii）该奖项反映了NSF的法定使命，通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。