闵可夫斯基时空的计算能力
The Computational Power of Minkowski Spacetime
摘要：
连接经典计算的两个端点的类时曲线的洛伦兹长度是通过闵可夫斯基时空的路径的函数。相关的运行时间差异是由于时间膨胀：观察者发现另一个物理上相同的理想时钟以不同的速度比自己的时钟滴答的现象。使用出现在计算复杂性理论的框架中的想法，时间膨胀被量化为一个算法资源，通过相关的相对论能量的$n$第阶多项式时间减少在完成观察者的旅程。这些结果使得量子计算的最佳二次\emph{Grover speedup}和使用经典计算机和相对论效应的$n=2$加速之间的比较成为可能。我们的目标不是提出一个实用的计算模型，而是探索物理学对计算的最终限制。
英文摘要：
The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
