OpenAI reports polynomial unitary synthesis with a Boolean oracle

For every n, one quantum oracle circuit generated in polynomial time from n using H, T, T† and CNOT approximates the channel of every n-qubit unitary to full diamond-norm error at most 1/2 after a suitable Boolean oracle is chosen; circuit size, qubits, queries and query length are polynomial in n.

Sources for this record

What was already known

Earlier oracle constructions addressed synthesis of a specified state. Coherent synthesis of an arbitrary unitary on every input with one uniformly generated polynomial circuit remained the Aaronson–Kuperberg constant-error problem.

AI involvement AI-led

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 Notable

Resolves the constant-error unitary-synthesis existence question in this Boolean-oracle model.

Limitations

The oracle may depend on the target unitary, and no efficient classical procedure constructs its truth table or circuit.

Technical verification Reported

Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.

Human understanding Few

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

2026-10-18 · publication

Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.

Read this published revision