AF: CQIS: Small: Theoretical Problems in Quantum Information

该项目解决了量子信息中的以下四个基本问题：(1)在量子边信息存在的情况下的随机性提取。为了确保通信安全，必须生成对手无法预测的密钥。这类密钥通常是通过随机性提取过程获得的，该过程将弱随机输入转换为(几乎)完全随机输出。团队正在研究实现这一任务的最有效方法，重点是在对手？S知道输入是量子的情况下。(2)量子密码散列函数(QCHASH)。散列函数是可用于验证消息的真实性和完整性的强大工具。量子散列函数通过使用量子态来扩展(经典)散列函数。一条经典的信息。该团队正在努力确定这些函数的优势，特别是在经典边信息被泄露给对手的情况下。(3)量子同态加密(QHE)。同态加密允许加密数据由多方处理，不需要解密，也不需要与数据所有者交互。当数据是量子的，并且假设对手是全能的时，团队正在寻找最有效的方法来实现这一任务。(4)组合优化的量子算法。实践中的许多优化问题，即使满足于一个近似的答案，也是极难解决的。该团队正在研究量子算法可以在多大程度上加快计算速度或提高近似质量。重点介绍了最近提出的量子近似优化算法(QAOA)的算法框架，这些问题的积极解决可能导致新的、强大的量子信息在保障信息安全和解决优化问题方面的应用。该项目还培养多名学生成为量子信息科学方面的专家。

This project addresses the following four sets of fundamental questions in quantum information.(1) Randomness extraction in the presence of quantum side information.To secure communication security, it is necessary to generate cryptographic keys that cannot be predicted by an adversary. Such keys are usually obtained through a randomness extraction process, which converts a weakly random input to a (almost) perfectly random output.The team is researching the most efficient methods for this task, with the focus on the setting that the adversary?s knowledge about the input is quantum.(2) Quantum cryptographic hash functions (qchash). Hash functions are powerful tools that can be used to verify the authenticity and the integrity of a message. Quantum hash functions extend (classical) hash functions by using a quantum state to ?tag? a classical message. The team is working to identify the advantages of such functions, especially in the scenario where classical side information is leaked to the adversary.(3) Quantum homomorphic encryption (QHE). Homomorphic encryption allows encrypted data to be processed by multiple parties without the need for decryption or for interactions with the owner of the data.The team is looking for the most efficient methods for achieving this task, when the data are quantum and the adversary is assumed to be all-powerful.(4) Quantum algorithms for combinatorial optimization. Many optimization problems from practice are extremely difficult to solve, even if one is content with an approximate answer. The team is examining to what extent quantum algorithms can speed up the computation or increase quality of approximation. A focus is on the recently proposed algorithmic framework of quantum approximate optimization algorithms (QAOA).Positive solutions to the above questions may lead to new and powerful quantum information applications for safeguarding information security and for solving optimization problems. The project also trains multiple students to become experts on quantum information science.