Dataset for Figure 1 and Figure 2 presented in "Strong dispersion property for the quantum walk on the hypercube" (preprint available at arxiv.org/abs/2201.11735). The rows of data.csv file contain the calculated quantities related to the quantum walk on the hypercube: the first row is the maximum probability of a vertex during a walk on the 50-dimensional hypercube; the second row contains the number of steps to minimize the aforementioned probability for various n; the third row is the maximum probability of a vertex after approximately 0.849n steps, for various n; the fourth row is the probability of the walker to be at the 0ⁿ vertex (n=50) during a walk on the 50-dimensional hypercube. The rows of aux.csv contain auxiliary data needed to plot the figures: the first row contains the integers 0 to 199 and corresponds to the variable 't' in Figure 1; the second row contains the integers from 1 to 200 and corresponds to the variable 'n' in Figure 2; the third row is the value of the linear function -0.754 + 0.849*n, depicted in the upper panel of Figure 2; the fourth row is the value of the function 5*1.93^(-n), depicted in the lower panel of Figure 2. To generate the figures, the following Matlab commands may be used (after loading the CSV files into variables aux and data):

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

Dataset for Figure 1 and Figure 2 presented in "Strong dispersion property for the quantum walk on the hypercube" (preprint available at arxiv.org/abs/2201.11735). The rows of data.csv file contain the calculated quantities related to the quantum walk on the hypercube: the first row is the maximum probability of a vertex during a walk on the 50-dimensional hypercube; the second row contains the number of steps to minimize the aforementioned probability for various n; the third row is the maximum probability of a vertex after approximately 0.849n steps, for various n; the fourth row is the probability of the walker to be at the 0ⁿ vertex (n=50) during a walk on the 50-dimensional hypercube. The rows of aux.csv contain auxiliary data needed to plot the figures: the first row contains the integers 0 to 199 and corresponds to the variable 't' in Figure 1; the second row contains the integers from 1 to 200 and corresponds to the variable 'n' in Figure 2; the third row is the value of the linear function -0.754 + 0.849*n, depicted in the upper panel of Figure 2; the fourth row is the value of the function 5*1.93^(-n), depicted in the lower panel of Figure 2. To generate the figures, the following Matlab commands may be used (after loading the CSV files into variables aux and data):

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

This is a data set for the paper "Quantum speedups for dynamic programming on n-dimensional lattice graphs", with the full version available at https://arxiv.org/abs/2104.14384. Each file SolverDAKB.nb contains the Mathematica code to find the complexity of the quantum algorithm for D=A, K=B. The solution for the corresponding can be read from the result of the minimization (after the line opt = NMinimize[args,{...}]). The variables from the Mathematica files correspond to the values in the paper as follows: Td corresponds to T_d. akd corresponds to α_k,d. R00 corresponds to x; Rki corresponds to x_k,i. At the end of each file, a list of the differences between the constraints is given. In all results, the negative differences (which correspond to constraint violation) are negligible (e.g, 10^-7) and can be eliminated by adding some small values to the point found by the minimization.

This is a data set for the paper "Quantum speedups for dynamic programming on n-dimensional lattice graphs", with the full version available at https://arxiv.org/abs/2104.14384. Each file SolverDAKB.nb contains the Mathematica code to find the complexity of the quantum algorithm for D=A, K=B. The solution for the corresponding can be read from the result of the minimization (after the line opt = NMinimize[args,{...}]). The variables from the Mathematica files correspond to the values in the paper as follows: Td corresponds to T_d. akd corresponds to α_k,d. R00 corresponds to x; Rki corresponds to x_k,i. At the end of each file, a list of the differences between the constraints is given. In all results, the negative differences (which correspond to constraint violation) are negligible (e.g, 10^-7) and can be eliminated by adding some small values to the point found by the minimization.