{"id":"openai-math/Exact-quantum-factoring-over-a-fixed-finite-gate-set","pdf":"https://github.com/openai/math/blob/main/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Exact-quantum-factoring-over-a-fixed-finite-gate-set-September-25-2026","tags":["quantum-computing","quantum-circuits","factoring"],"score":0,"title":"Exact quantum factoring over a fixed finite gate set","domain":"Mathematical physics","family":"279","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We give a polynomial-time uniform quantum circuit family that outputs the complete prime factorization of every integer N ≥ 2 with probability one. A fixed finite set of bounded-arity gates suffices, and both the gate count and the number of qubits have polynomial worst-case bounds in the input length.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Exact quantum factoring over a fixed finite gate set"}