Coined quantum walks on percolation graphs

Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing properties of quantum walks compared with their classical counterparts have been well-studied on regular structures and also shown to be sensitive to defects and imperfections in the lattice. As a simple example of a disordered system, we consider percolation lattices, in which edges or sites are randomly missing, interrupting the progress of the quantum walk. We use numerical simulation to study the properties of coined quantum walks on these percolation lattices in one and two dimensions. In one dimension (the line) we introduce a simple notion of quantum tunneling and determine how this affects the properties of the quantum walk as it spreads. On two-dimensional percolation lattices, we show how the spreading rate varies from linear in the number of steps down to zero, as the percolation probability decreases to the critical point. This provides an example of fractional scaling in quantum walk dynamics.Comment: 25 pages, 14 figures; v2 expanded and improved presentation after referee comments, added extra figur

Deliverable Raport D4.6 Tools for generating QMRF and QPRF reports

Scientific reports carry significant importance for the straightforward and effective transfer of knowledge, results and ideas. Good practice dictates that reports should be well-structured and concise. This deliverable describes the reporting services for models, predictions and validation tasks that have been integrated within the eNanoMapper (eNM) modelling infrastructure. Validation services have been added to the Jaqpot Quattro (JQ) modelling platform and the nano-lazar read-across framework developed within WP4 to support eNM modelling activities. Moreover, we have proceeded with the development of reporting services for predictions and models, respectively QPRF and QMRF reports. Therefore, in this deliverable, we first describe the three validation schemes created, namely training set split, cross- and external validation in detail and demonstrate their functionality both on API and UI levels. We then proceed with the description of the read across functionalities and finally, we present and describe the QPRF and QMRF reporting services