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Register a new userThe Grover search as a naturally occurring phenomenon
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Added by
Giuseppe Di Molfetta Prof.
Publication date
2019
fields
Physics
and research's language is
English
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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.
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The exfoliation of two naturally occurring van der Waals minerals, graphite and molybdenite, arouse an unprecedented level of interest by the scientific community and shaped a whole new field of research: 2D materials research. Several years later, the family of van der Waals materials that can be exfoliated to isolate 2D materials keeps growing, but most of them are synthetic. Interestingly, in nature plenty of naturally occurring van der Waals minerals can be found with a wide range of chemical compositions and crystal structures whose properties are mostly unexplored so far. This Perspective aims to provide an overview of different families of van der Waals minerals to stimulate their exploration in the 2D limit.
The fabrication of van der Waals heterostructures, artificial materials assembled by individually stacking atomically thin (2D) materials, is one of the most promising directions in 2D materials research. Until now, the most widespread approach to stack 2D layers relies on deterministic placement methods which are cumbersome when fabricating multilayered stacks. Moreover, they tend to suffer from poor control over the lattice orientations and the presence of unwanted adsorbates between the stacked layers. Here, we present a different approach to fabricate ultrathin heterostructures by exfoliation of bulk franckeite which is a naturally occurring and air stable van der Waals heterostructure (composed of alternating SnS2-like and PbS-like layers stacked on top of each other). Presenting both an attractive narrow bandgap (<0.7 eV) and p-type doping, we find that the material can be exfoliated both mechanically and chemically down to few-layer thicknesses. We present extensive theoretical and experimental characterizations of the materials electronic properties and crystal structure, and explore applications for near-infrared photodetectors (exploiting its narrow bandgap) and for p-n junctions based on the stacking of MoS2 (n-doped) and franckeite (p-doped)
A sequential application of the Grover algorithm to solve the iterated search problem has been improved by Ozhigov by parallelizing the application of the oracle. In this work a representation of the parallel Grover as dynamic system of inversion about the mean and Grover operators is given. Within this representation the parallel Grover for $k = 2$ can be interpreted as rotation in three-dimensional space and it can be shown that the sole application of the parallel Grover operator does not lead to a solution for $k > 2$. We propose a solution for $k = 3$ with a number of approximately $1.51sqrt{N}$ iterations.
We investigate the role of quantum coherence depletion (QCD) in Grover search algorithm (GA) by using several typical measures of quantum coherence and quantum correlations. By using the relative entropy of coherence measure ($mathcal{C}_r$), we show that the success probability depends on the QCD. The same phenomenon is also found by using the $l_1$ norm of coherence measure ($mathcal{C}_{l_1}$). In the limit case, the cost performance is defined to characterize the behavior about QCD in enhancing the success probability of GA, which is only related to the number of searcher items and the scale of database, no matter using $mathcal{C}_r$ or $mathcal{C}_{l_1}$. In generalized Grover search algorithm (GGA), the QCD for a class of states increases with the required optimal measurement time. In comparison, the quantification of other quantum correlations in GA, such as pairwise entanglement, multipartite entanglement, pairwise discord and genuine multipartite discord, cannot be directly related to the success probability or the optimal measurement time. Additionally, we do not detect pairwise nonlocality or genuine tripartite nonlocality in GA since Clauser-Horne-Shimony-Holt inequality and Svetlichnys inequality are not violated.
Understanding language requires grasping not only the overtly stated content, but also making inferences about things that were left unsaid. These inferences include presuppositions, a phenomenon by which a listener learns about new information through reasoning about what a speaker takes as given. Presuppositions require complex understanding of the lexical and syntactic properties that trigger them as well as the broader conversational context. In this work, we introduce the Naturally-Occurring Presuppositions in English (NOPE) Corpus to investigate the context-sensitivity of 10 different types of presupposition triggers and to evaluate machine learning models ability to predict human inferences. We find that most of the triggers we investigate exhibit moderate variability. We further find that transformer-based models draw correct inferences in simple cases involving presuppositions, but they fail to capture the minority of exceptional cases in which human judgments reveal complex interactions between context and triggers.
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