Depth-1 distinctness for pseudorandom unitaries
A single layer of independent random single-qubit Clifford gates is -distinct for polynomially many queries. Consequently, in the pseudorandom-unitary construction, the depth- global unitary -design layer can be replaced by a depth-1 tensor product of single-qubit -designs while retaining the distinctness property needed for the construction. This provides a counterexample to the conjecture that every negligibly distinct ensemble must be entangling.
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Quantum pseudorandomness
- Posed by
- Raza, Eisert and Fefferman (the authors' own working conjecture)
- Year posed
- —
- Years open
- —
- Solved
- 2026-09-02
- Model
- ChatGPT 5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Asad Raza, Jens Eisert, Bill Fefferman
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 6 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
The paper proves that a tensor-product ensemble of independently chosen single-qubit Clifford gates is -distinct when the number of queries is polynomial in . This disproves the authors' conjecture that negligibly distinct ensembles must necessarily be entangling. As an application, the depth- global Clifford/unitary--design layer used in the pseudorandom-unitary construction can be replaced by a single depth-1 layer of local single-qubit -designs while preserving the required distinctness property.
What the AI did
The authors state that Proposition III.5 was proposed by ChatGPT 5.6 Sol as a counterexample to their conjecture that a -distinct ensemble must be entangling. Sol identified that a single layer of independent random single-qubit Clifford gates is already negligibly distinct for polynomially many queries. ChatGPT 5.5 and 5.6 Pro were also used to devise proof strategies for the paper's main results, as well as for literature search, exposition, and technical checking; all proofs were independently verified by the authors.
Verification
The result appears as Proposition III.5 in a coauthored research paper by Asad Raza, Jens Eisert, and Bill Fefferman. The authors explicitly state that ChatGPT 5.6 Sol proposed the counterexample and that they independently verified all proofs. No formal proof-assistant certificate is reported.
Source
- PaperarXiv
Submitted by VibeGene on