We provide first evidence that under certain conditions, 1/2-spin fermions
may naturally behave like a Grover search, looking for topological defects in a
material. The theoretical framework is that of discrete-time quantum walks
(QW), i.e. local unitary matrices that drive the evolution of a single particle
on the lattice. Some QW are well-known to recover the $(2+1)$--dimensional
Dirac equation in continuum limit, i.e. the free propagation of the 1/2-spin
fermion. We study two such Dirac QW, one on the square grid and the other on a
triangular grid reminiscent of graphene-like materials. The numerical
simulations show that the walker localises around the defects in $O(\sqrt{N})$
steps with probability $O(1/\log{N})$, in line with previous QW search on the
grid. The main advantage brought by those of this paper is that they could be
implemented as `naturally occurring' freely propagating particles over a
surface featuring topological---without the need for a specific oracle step.
From a quantum computing perspective, however, this hints at novel applications
of QW search : instead of using them to look for `good' solutions within the
configuration space of a problem, we could use them to look for topological
properties of the entire configuration space.

本研究提供了第一份证据表明，在特定条件下，1/2 自旋费米子可以自然地表现出 Grover 搜索，在材料中寻找拓扑缺陷。作者还研究了两个 Dirac 量子行走模型，并展示了与先前的量子行走搜索一致的步数复杂度。

Grover 搜索作为自然现象

The Grover search as a naturally occurring phenomenon

The theory of phase ordering dynamics -- the growth of order through domain
coarsening when a system is quenched from the homogeneous phase into a
broken-symmetry phase -- is reviewed, with the emphasis on recent developments.
Interest will focus on the scaling regime that develops at long times after the
quench. How can one determine the growth laws that describe the time-dependence
of characteristic length scales, and what can be said about the form of the
associated scaling functions? Particular attention will be paid to systems
described by more complicated order parameters than the simple scalars usually
considered, e.g. vector and tensor fields. The latter are needed, for example,
to describe phase ordering in nematic liquid crystals, on which there have been
a number of recent experiments. The study of topological defects (domain walls,
vortices, strings, monopoles) provides a unifying framework for discussing
coarsening in these different systems.

本文回顾了相变动力学理论，重点是最近的进展，并探讨了长时间后呈现的缩放规律及特征长度尺度的生长规律，特别关注了使用矢量和张量场等更复杂的序参量描述的系统。本文以研究拓扑缺陷为基础，提供了一个统一的框架来讨论这些不同系统中的相序演化。