Open Problems in Quantum Mechanics for humans and AI Agents

A curated catalogue of open problems in quantum theory — for humans and AI agents to attack, discuss, and make progress on.

This is a collaborative, community project. If you spot an error, know of a result that should update a problem's status, or want to add a problem, reference, or piece of context: contributions are very welcome, just open a pull request or an issue.

Website

https://openquantumproblems.com/

Timeline

4 September 2026 — full catalogue review implemented

• Reassessed all 111 original entries and implemented their statement, scope, status and citation corrections. The full audit records the pre-change findings; the implementation record maps the changes.
• Consolidated nine overlapping entries and moved U5 to background. All original #p/ID links remain valid; archived pages link to their active parents and are excluded from active counts.
• Added or promoted twelve questions: M12/M13, B13/B14/B15, E16, N11, C11/C12, A19, QF11 and O10. The catalogue now has 113 active entries and ten retained archive/background pages.
• Added source-linked evidence badges, a separate author-provenance section, relations, review dates, a public review/evidence-policy page and a non-counted research watchlist.
• Linked all 401 reference records and corrected additional legacy author/title/publication metadata while preserving the literature history.
• Added the frontend credit “powered by Astra”. Preserved the existing site design and GitHub publishing workflow.
• Added automated checks for all IDs, archive targets, source metadata, internal links, KaTeX expressions and rendering of every detail/category view.

4 September 2026 — earlier literature update

• A5: added the first quantum-oracle separation between $\mathsf{QMA}(2)$ and $\mathsf{QMA}$ and the resulting constant-error no-disentanglers theorem.
• A12/A14/A16/A17/A18: added new BosonSampling hardness ingredients, the withdrawal of a claimed graph-isomorphism algorithm, an independent bounded-round query-simulation theorem, a shadow-tomography obstruction, and fault-tolerance overhead, calibration and decoding results.
• C6/C7: recorded the improved $C_7$ zero-error lower bound and the counterexample to the optimality of Marton's classical broadcast-channel inner bound.
• E4/E6/E10/E11: added a finite-round LOCC criterion for multiqubit product bases, correlated-catalytic irreversibility, and the nonadditivity/additivity split for Rényi entanglement of purification away from the von Neumann case.
• N3/N8: added the composite-dimension MUB numerical survey and size-independent multipartite GHZ self-testing robustness.
• O5/O9 and F2/F8/F9: added Pauli-twirling non-Markovianity, scalable noise-learning methods, a revised categorical Born-rule theorem, compositional quantum-reference-frame results, and a sharper taxonomy of dynamical causal order.
• These were partial-progress records, not independently verified solutions. The subsequent full review corrected scope, metadata and provenance errors in this initial update; current entry wording takes precedence.

20 August 2026

• C4: recorded a preprint claiming exponential strong converses for all finite-dimensional degradable and antidegradable channels.
• E1/E2: added new two- and three-copy distillability results, while keeping the general NPT and $n\geq3$ Werner questions open.
• E14/N2: recorded preprint classification/construction claims for $\mathrm{AME}(7,d)$, five other AME cases and order-six complex Hadamard matrices; the MUB problem is distinct.
• C1/A16: added a certified positive-capacity lower benchmark for the depolarizing channel, not its exact threshold, and a bounded-round quantum-query simulation preprint.
• Added three previously missing problems: quantum property testing (A17), fault tolerance beyond local stochastic noise (A18), and learning open-system dynamics (O9).
• Checked and summarized each paper's author-declared AI involvement, conditionally and without treating it as independently verified.

29 July 2026

• E2: recorded preprints claiming the two-copy Werner-state result; the general all-copy question remains open.
• C1/E3: added the new non-PPT/non-antidegradable zero-capacity channel and constant-gap separability algorithm.
• N6/N9: added the three finite-level NPA non-exactness and phase-transition results.
• C4/A5/A9/B11: added the stabilizer-code strong converse, optimal product-test analysis, and VGP/stoquasticity results.
• Added reported AI-provenance disclosures to improved entries, with explicit uncertainty and human-verification caveats.

Contributing

• Fix or expand a problem: edit the relevant file in app/data/.
• Add a solution, improvement, or progress note: same place, with the contributor's name and (if applicable) the model used.
• Anything else — new problems, better references, corrections — PRs welcome.

No formal process, no gatekeeping. Just send it.

Catalogue structure and evidence

The source of truth is app/data/cat-*.js, aggregated by app/data/problems.js. main.tex is a historical manuscript, not a synchronized export of the current site. Do not renumber existing IDs or reuse an archived ID for a new question.

• statement defines the model, assumptions, quantifiers and success criterion; context separates the established baseline from the open residual.
• horizon distinguishes sharp, incremental, programme and conceptual entries. A programme is not a single conjecture.
• status: "improved" means partial progress is recorded; it does not certify every cited claim.
• evidence contains { kind, summary, url, date?, version? }. Supported kinds are published, preprint, numerical, conjecture and withdrawn. Include scope, not just an optimistic headline.
• provenance contains { summary, url, version? } for attributed disclosures. No disclosure is not evidence of no AI use, and AI use is not evidence for or against mathematical correctness.
• relations contains { id, type } with parent, benchmark, reduction or related.
• archive contains { kind: "merged" | "background", targets: [id], reason }. Archived pages remain addressable through getProblem; PROBLEMS and category counts include only active records.
• References should use verified DOI/arXiv/publisher URLs. Distinguish submission, revision, acceptance and publication dates; do not infer publication from an arXiv identifier or acceptance notice.

Development checks

Run npm test for catalogue integrity, mathematical syntax and server-rendered view checks, then npm run build for the production build. npm run dev starts the normal local preview. The test suite uses the project's existing Next compiler and React renderer; it requires no extra browser or test dependencies.