The numerical results for the complexity of the quantum algorithm for dynamic programming on n-dimensional lattice graph

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.