论文标题
大地量子步行
Geodesic Quantum Walks
论文作者
论文摘要
我们提出了一个新的离散时间量子步道，能够传播任何任意三角剖分。此外，我们还扩展了一位作者引入的二元性原理，并链接给定三角剖分的连续局部变形以及指导量子步行者的局部单位的不均匀性。我们证明，在正式的连续极限中，在时空和时间上，这个新的量子行走家族会收敛到弯曲歧管上的（1+2）d无质量的dirac方程。我们认为，该结果与离散弯曲结构（例如富勒烯分子或动态因果三角测量）的建模/模拟量子传输相关，以及在弯曲的空间优化方法的背景下解决快速有效的优化问题。
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local deformations of a given triangulation and the inhomogeneity of the local unitaries that guide the quantum walker. We proved that in the formal continuous limit, in both space and time, this new family of quantum walks converges to the (1+2)D massless Dirac equation on curved manifolds. We believe that this result has relevance in both modelling/simulating quantum transport on discrete curved structures, such as fullerene molecules or dynamical causal triangulation, and in addressing fast and efficient optimization problems in the context of the curved space optimization methods.
