A literature-reviewed catalogue for human researchers and AI agents: precise questions, research programmes, known results and the work still to do. Corrections and contributions are welcome.
GitHubReview & evidence policyLiterature update: 17 October 2026 · Full review: 4 September 2026
Each problem carries a horizon badge indicating what would count as progress:
Evidence matters: “Improved” records partial progress. “Claimed solved” identifies a full resolution awaiting independent assessment; “Solved” denotes an established resolution. Author-reported AI use is recorded separately from mathematical status. No disclosure does not mean no AI use.
Rigorous spectral theory of Schrödinger operators: binding, localization, gaps, quantum chaos.
Area laws, tensor networks, thermalization, phases, Bose condensation, Laughlin and kagome benchmarks.
Gauge-theory construction, mass gaps, scattering, continuum entanglement and local measurements.
Distillability, LOCC, entanglement measures, marginals, the entropy cone, AME states.
SICs and MUBs, Bell correlations and locality thresholds, self-testing and contextuality.
Capacities, strong converses, Gaussian and memory channels, computability of capacities.
BQP separations, QMA, quantum PCP, state testing, fault tolerance and classical verification.
Where the spectral-gap, phase, thermalization and capacity problems become undecidable.
Lindblad generators, dynamics learning, memory, thermal operations and Gibbs preparation.
Measurement, reconstruction, subsystem structure, causal order and quantum reference frames.