Fundamental unavoidability of exponential measurement overhead in circuit knitting

Determine whether exponential scaling of the number of measurements with respect to the number of cut locations is fundamentally unavoidable for circuit knitting methods that decompose large quantum computations into smaller subcircuits and reconstruct expectation values via classical post-processing.

Background

Circuit knitting techniques (including wire- and gate-cutting within the quasiprobability framework) typically induce a sampling overhead that grows exponentially in the number of cut locations, due to rescaling factors in the unbiased estimators. While this paper demonstrates that tree-structured circuits can circumvent this behavior via tomography-based constructions, it does not settle the general case.

Establishing whether exponential scaling is intrinsic to circuit knitting across broader circuit classes and cutting schemes is central to assessing the theoretical limits and practical viability of these methods on near-term and future quantum architectures.