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.

System	Parameter	Value	Notes
2-Spin	State space dimension	16 × 500	Sparse matrix representation fits into the L2 cache—polyadic processing is slower, memory footprint improvement is not significant
	nnz(L) and wct(Lv)^a, sparse	116,000, 0.5 ms
	nnz(L) and wct(Lv)^a, polyadic	12,000, 5 ms
4-Spin	State space dimension	256 × 500	Sparse matrix representation exceeds L2 cache, parity on the wall clock time, significant memory advantage for the polyadic format
	nnz(L) and wct(Lv)^a, sparse	2,600,000, 13 ms
	nnz(L) and wct(Lv)^a, polyadic	14,000, 18 ms
6-Spin	State space dimension	4096 × 500	Sparse matrix representation is in the gigabytes, polyadic processing is faster and offers a vast memory footprint advantage
	nnz(L) and wct(Lv)^a, sparse	37,000,000, 227 ms
	nnz(L) and wct(Lv)^a, polyadic	87,000, 185 ms

^aIntel Xeon E5-2698, single core.