What was already known
Parity has classical constant-depth circuit lower bounds. The corresponding measured-output quantum setting with polynomially many zero-initialized ancillas and unrestricted final garbage remained Moore’s parity conjecture.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves Moore’s QAC⁰ parity conjecture under the stated measured-output circuit model.
Limitations
The lower bound is worst-case over inputs and assumes constant depth, polynomially many qubits, zero-initialized ancillas and one measured output qubit.
Technical verification
OpenAI reports a Lean proof matching the selected claim.
Formal checking
The pinned Lean note proves this parity consequence, including a strict-below-2/3 specialization.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- For every fixed depth, polynomial qubit bound and ε>0, sufficiently large measured-output quantum circuits using arbitrary one-qubit and unbounded-arity Toffoli gates have some input on which parity succeeds with probability below 1/2+ε.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision