Analytical incompatibility certification for general circuit architectures

Establish whether general quantum circuit architectures can be ruled out analytically when the target unitary is a Clifford operation.

Background

The paper develops fidelity-based architecture witnesses for certifying that a target unitary cannot be implemented within a prescribed circuit architecture. For Clifford target unitaries, the authors derive analytical bounds for staircase architectures with specified no-signalling relations by exploiting stabiliser-state representations and counting Bell pairs across suitable bipartitions. The unresolved problem is to extend this analytical certification method to arbitrary circuit architectures, including architectures that allow signalling between all input and output systems.