Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 274-01. Product-projection localization and the QAC0 parity lower bound
Manuscript map · lines 7955–7964
OpenAI@2026-10-07#rem:oai-p-274-01
Authors: OpenAI. Family 274.
Title: Product-projection localization and the QAC0 parity lower bound.
Abstract: We prove that constant-depth quantum circuits with arbitrary one-qubit and unbounded-arity Toffoli gates cannot compute parity with any fixed positive worst-case advantage using polynomially many qubits. Ancillas start in zero, only one output qubit is measured, and all final garbage is unrestricted. This resolves Moore's parity conjecture in the measured-output model.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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