Dataset for "Strong dispersion property for the quantum walk on the hypercube"

<p>Dataset for <em>Figure 1</em> and <em>Figure 2</em> presented in &quot;<a href="https://doi.org/10.1088/1751-8121/aca6b9">Strong dispersion property for the quantum walk on the hypercube</a>&quot; (preprint available at <a href="http://arxiv.org/abs/2201.11735">arxiv.org/abs/2201.11735</a>).</p> <p>The rows of <em>data.csv</em> file contain the calculated quantities related to the quantum walk on the hypercube:</p> <ul> <li>the first row is the maximum probability of a vertex during a walk on the 50-dimensional hypercube;</li> <li>the second row contains the number of steps to minimize the aforementioned probability for various <em>n</em>;</li> <li>the third row is the maximum probability of a vertex after approximately 0.849<em>n</em> steps, for various <em>n</em>;</li> <li>the fourth row is the probability of the walker to be at the 0<em>ⁿ</em> vertex (<em>n</em>=50) during a walk on the 50-dimensional hypercube.</li> </ul> <p>&nbsp;</p> <p>The rows of <em>aux.csv</em> contain auxiliary data needed to plot the figures:</p> <ul> <li>the first row contains the integers 0 to 199 and corresponds to the variable &#39;<em>t</em>&#39; in Figure 1;</li> <li>the second row contains the integers from 1 to 200 and corresponds to the variable &#39;<em>n</em>&#39; in Figure 2;</li> <li>the third row is the value of the linear function -0.754 + 0.849*<em>n</em>, depicted in the upper panel of Figure 2;</li> <li>the fourth row is the value of the function 5*1.93^(-<em>n</em>), depicted in the lower panel of Figure 2.</li> </ul> <p>&nbsp;</p> <p>To generate the figures,&nbsp; the following Matlab commands may be used (after loading the CSV files into variables <em>aux</em> and <em>data</em>):</p> <pre><code>figure; scatter(aux(1,:),data(1,:),15); set(gca,'YScale','log') % F1: upper figure; scatter(aux(1,1:2:end),data(1,1:2:end),15); hold on; scatter(aux(1,:),data(4,:),15,'s'); hold off; set(gca,'YScale','log') % F1: lower figure; scatter(aux(2,:),data(2,:),15); hold on; plot(aux(2,:),aux(3,:)); xlim([0,100]);hold off; %F2: upper figure; scatter(aux(2,:),data(3,:),15);set(gca,'YScale','log'); hold on; semilogy(aux(2,:), aux(4,:));hold off; xlim([0,100]); %F2: lower</code></pre> <p>&nbsp;</p>