OpenAI · 283-01 · 2026-10-05 · Mathematical physics
Polynomial-Time Unitary Synthesis from a Boolean Oracle
preprints/Polynomial-Time-Unitary-Synthesis-from-a-Boolean-Oracle-October-5-2026
Family 283. Polynomial-time, constant-error unitary synthesis from a Boolean oracle.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Solves the constant-error Aaronson–Kuperberg unitary synthesis problem: a uniform polynomial-size quantum oracle circuit approximates every -qubit unitary channel within diamond-norm error , after a suitable Boolean oracle is chosen. Gates, qubits, oracle calls and query length are polynomially bounded. The target-dependent oracle may have an unrestricted truth table; its efficient classical construction is not asserted.
We give a positive answer to the constant-error formulation of the Aaronson–Kuperberg unitary synthesis problem. For every n, a quantum oracle circuit generated in polynomial time from n alone can approximate the channel of every n-qubit unitary to full diamond-norm error at most 1/2, after a suitable Boolean oracle is chosen. Using the fixed gates , the circuit has polynomially many qubits, elementary gates, and oracle calls, and its oracle queries have polynomial length. The oracle may depend on the target unitary; the theorem does not give an efficient classical procedure for constructing it.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.