Figure 4
From: Taming numerical errors in simulations of continuous variable non-Gaussian state preparation
Verification of the \(\mathop {\mathrm {trunc}}\nolimits _{201} \{{\hat{D}}(3 - 2\imath )\}\) matrix approximated using (a) TAME (\(d_{0} = 201\) and \(d_{1} = 277\)) and (b) plain matrix exponential (\(d_{0} = 201\)). Blue lines mark the row-wise \({{\,\mathrm{mean}\,}}_{i}(L_{ij})\) values, light-blue region stretches a standard deviation \({{\,\mathrm{std}\,}}_{i}(L_{ij})\) away from the mean. The maximal difference \(\max _{i}(L_{ij})\) within each column is represented by the red line. The dashed horizontal line corresponds to the unit round-off in double precision floating point number representation. (a) The matrix is structurally correct. The average differences are negligible, their values falling below the unit round-off. The maximal differences match up to 11 decimal places. (b) The matrix maintains correct structure in its first third. The truncation errors manifest in the rest of the matrix as an exponential explosion in the maximal difference (around the 100th column) and a steady rise in the mean value.
