Avoiding exponential scaling without relaxing typical device constraints

Establish whether the exponential sampling-overhead scaling in the number of circuit cuts can be avoided without significantly relaxing the local-device constraints typically assumed in circuit knitting, even for restricted graph families.

Background

Prior work has explored reducing sampling overhead in circuit cutting by optimizing cut placement and improving quasiprobability decompositions, but these approaches still incur exponential dependence on the number of cuts in general. Whether one can bypass this scaling without altering the standard locality and device assumptions has been unclear.

This paper shows that for tree-structured circuits, polynomial scaling is achievable under typical device constraints, leaving open the broader question of whether similar improvements extend beyond trees without relaxing assumptions.