AF: CQIS: Small: Theoretical Problems in Quantum Information

该项目解决了量子信息中的以下四组基本问题。(1)存在量子侧信息的随机性提取。为了确保通信安全，有必要生成对手无法预测的加密密钥。这种密钥通常通过随机提取过程获得，该过程将弱随机输入转换为（几乎）完全随机输出。该团队正在研究最有效的方法来完成这项任务，重点是设置对手？S关于输入的知识是量子的。(2)量子密码哈希函数（qchash）。哈希函数是强大的工具，可用于验证消息的真实性和完整性。量子哈希函数通过使用量子态来标记来扩展（经典）哈希函数。经典的信息。该团队正在努力确定这些函数的优点，特别是在经典的侧信息泄露给对手的情况下。(3)量子同态加密（QHE）。同态加密允许多方处理加密的数据，而不需要解密或与数据所有者交互。该团队正在寻找最有效的方法来完成这项任务，当数据是量子的，对手被认为是无所不能的。(4)组合优化的量子算法。实践中的许多优化问题是极难解决的，即使人们满足于一个近似的答案。该团队正在研究量子算法能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）算法框架。对上述问题的积极解决可能会带来新的强大的量子信息应用，以保障信息安全和解决优化问题。该项目还培养了多名学生成为量子信息科学专家。

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.