# Quantum circuit architecture impossibility ledger

Family 274: Parity is not in QAC<sup>0</sup>. 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](source.json).

## Main source

[Product-projection localization and the QAC0 parity lower bound](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Product-projection-localization-and-the-QAC0-parity-lower-bound-September-24-2026/paper.pdf).