Each problem states how progress is verified and what counts as a contribution. Besides the problems curated here, the catalogue includes open conjectures from Formal Conjectures (with Lean statements), optimization constants and the AlphaEvolve problems. Know one that belongs here? Propose a problem.
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Map the boundary of classical simulability for quantum-advantage random circuit sampling experiments by improving tensor-network and other classical algorithms, with reproducible cost estimates and fidelity benchmarks.
Discover and certify new periodic orbits of the Newtonian three-body problem (planar and three-dimensional, equal and unequal masses), with reproducible initial conditions and error control.
Sharpen the rigorous numerical bounds on the scaling dimensions Δσ and Δε of the 3D Ising conformal field theory, and reconcile them with Monte Carlo estimates.
Combine public NICER pulse-profile posteriors, gravitational-wave tidal-deformability constraints and pulsar masses into reproducible, well-calibrated constraints on the neutron-star equation of state.
Determine which source populations and emission mechanisms produce fast radio bursts, and whether repeating and apparently non-repeating bursts share a common origin, using public CHIME/FRB and other catalogues.
Improve reproducible, circuit-level-noise thresholds and logical error rates for surface codes and quantum LDPC codes through better codes, syndrome circuits and decoders, benchmarked with open simulators such as Stim.
