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.

References

We leave as an interesting open question whether general circuit architectures can be ruled out analytically when the target unitary is a Clifford operation.

— Witnessing the architecture of quantum circuits  (2608.13169 - Mothe et al., 13 Aug 2026) in Conclusion, Section sec:conclusion

This raises a natural question: are there structured classes of active dependencies for which these additional sign constraints can nevertheless be resolved analytically?

— Such stuff as magic is made on: compact operator algebra, stabilizer polytope and the structure of reduced density matrices in a Kitaev spin liquid  (2609.03485 - Sabharwal et al., 3 Sep 2026) in Section 6.4, “Restricted observables and measurement resources”