{"id":"openai-math/Regular-trajectories-pruning-and-quantum-parity","pdf":"https://github.com/openai/math/blob/main/preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Regular-trajectories-pruning-and-quantum-parity-September-24-2026","tags":["quantum-computing","circuit-complexity","parity"],"score":0,"title":"Regular trajectories, pruning and quantum parity","domain":"Mathematical physics","family":"274","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove that constant-depth quantum circuits with arbitrary one-qubit gates and unbounded-arity Toffoli gates cannot compute parity with any fixed positive worst-case advantage using polynomially many total qubits. Ancillary qubits are initialized to $`|0\\rangle`$, one output qubit is measured, and all other final registers may be discarded without restriction. This resolves Moore's parity conjecture in the measured-output model.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Parity is not in QAC 0"}