Figure 9.

Visualization of different contraction orders on the DJ circuit. The contraction order is encoded in the color spectrum from green (contracted first) to purple (contracted last). (a) A simple contraction from left to right; (b–e) our two heuristics and the two other heuristics implemented in cotengra, specifically: (b) lookahead heuristic; (c) counting heuristic; (d) cotengra’s Betweenness heuristic; (e) cotengra’s RandomGreedy heuristic; (f) the heuristic used in [25], which exploits the fact that the tensor network originates from two circuits and contracts corresponding gates proportionally from the inside out.