Complexity characterization beyond tree-structured circuits

Characterize the measurement and resource complexity of tomography-based circuit knitting approaches for more general circuit architectures beyond trees, including planar graphs, circuits of bounded treewidth, and tensor-network amenable structures.

Background

The present work establishes polynomial measurement scaling for expectation-value estimation on tree-structured circuits via concatenated tomography and rescaling-free cuts. Extending these guarantees to broader architectures would clarify the scope of applicability and potential advantages of learning-based circuit knitting.

Identifying the regimes and graph structures where polynomial scaling persists, and quantifying resource trade-offs for non-tree topologies, are essential next steps to translate these methods to more general quantum computations.