论文标题
分析量子退火的最短矢量问题以搜索激发态
Analysis of the shortest vector problems with the quantum annealing to search the excited states
论文作者
论文摘要
最短的向量问题（SVP）是晶格问题之一，是基于晶格的密码学的数学基础，这有望是量子后加密。可以将SVP映射到ISIN问题上，原则上可以通过量子退火（QA）解决。但是，使用QA解决SVP的一个问题是，SVP的解决方案对应于哈密顿量问题的第一个激发态。因此，搜索接地状态的质量检查无法提供高概率的解决方案。在本文中，我们建议采用对质量保证的激动搜索来解决最短的向量问题。我们从数字上表明，激发状态搜索提供的解决方案的概率高于基本搜索。
The shortest vector problem (SVP) is one of the lattice problems and is mathematical basis for the lattice-based cryptography, which is expected to be post-quantum cryptography. The SVP can be mapped onto the Ising problem, which in principle can be solved by quantum annealing (QA). However, one issue in solving the SVP using QA is that the solution of the SVP corresponds to the first excited state of the problem Hamiltonian. Therefore, QA, which searches for ground states, cannot provide a solution with high probability. In this paper, we propose to adopt an excited-state search of the QA to solve the shortest vector problem. We numerically show that the excited-state search provides a solution with a higher probability than the ground-state search.
