Quantum circuit architecture impossibility ledger

Family 274: Parity is not in QAC⁰. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Compiler researchers can flag parity or majority targets that exceed the stated constant-depth measured-output circuit model.

Applicability and commercial boundary

The result is worst-case and assumes particular gates, polynomial qubits and zero ancillas. Other gate models, depth growth or restricted input distributions are not excluded.

Initial business decision

Research infrastructure. Buyer budget, commercial novelty and profitability are unvalidated.

Next verification action

Represent the exact circuit resource model and compare a proposed architecture against it.

Evidence scope

The catalog statement was individually reviewed. This record does not imply a manuscript proof review or formal-scope comparison. No independent Lean check was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Main source

Product-projection localization and the QAC0 parity lower bound.