Table 4 Evolution generator dimension (spin × spatial), number of nonzeroes (nnz), and matrix-vector multiplication wall clock time (wct) statistics for a series of simulations of ultrafast “maximum-quantum” experiments (70) that include the effect of isotropic spatial diffusion using seven-point central finite difference operators.

2-SpinState space dimension16 × 500Sparse matrix representation fits into the L2 cache—polyadic processing is slower,
memory footprint improvement is not significant
nnz(L) and wct(Lv)a, sparse116,000, 0.5 ms
nnz(L) and wct(Lv)a, polyadic12,000, 5 ms
4-SpinState space dimension256 × 500Sparse matrix representation exceeds L2 cache, parity on the wall clock time, significant
memory advantage for the polyadic format
nnz(L) and wct(Lv)a, sparse2,600,000, 13 ms
nnz(L) and wct(Lv)a, polyadic14,000, 18 ms
6-SpinState space dimension4096 × 500Sparse matrix representation is in the gigabytes, polyadic processing is faster and
offers a vast memory footprint advantage
nnz(L) and wct(Lv)a, sparse37,000,000, 227 ms
nnz(L) and wct(Lv)a, polyadic87,000, 185 ms

aIntel Xeon E5-2698, single core.