The Fractional Colouring Conjecture for Triply Efficient Pauli Shadow Tomography
Conjecture 13 of King, Gosset, Kothari and Babbush asserts that for the set of Pauli observables with expectation value at least in magnitude, the fractional chromatic number of the induced anticommutation graph is ; it would give a triply efficient Pauli shadow tomography algorithm. False: there are states and observables for which no finite constant bounds .
- Result
- Disproved
- Status
- Candidate (review pending)
- AI contribution
- AI co-developed
- Method
- Construction
- Field
- Shadow tomography
- Posed by
- Robbie King, David Gosset, Robin Kothari and Ryan Babbush
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-08-20
- Model
- GPT Sol 5.6
- Vendor
- OpenAI
- Collaborators
- Jędrzej Stempin, Santiago Llorens, Felix Huber
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 16 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The arXiv comments field reads "Found with GPT Sol 5.6", and the paper's AI statement says the model was used to derive the main results, Theorem A and Theorem B. The construction amplifies fractional chromatic numbers, beta numbers and expectation values through lexicographic graph products.
Verification
Checked by this site on 21 August 2026 against the paper (arXiv:2608.20113v1, 14pp): the refuted statement is Conjecture 13 of King, Gosset, Kothari and Babbush in PRX Quantum 6, 010336 (2025), and the AI statement is as quoted. The constructions were not checked here. Days-old preprint, no independent review.