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.
11 shown
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.
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.
Prove that a symmetric informationally complete POVM (d^2 equiangular lines in C^d) exists in every dimension d, and extend the list of dimensions with exact or numerical solutions.
Determine reliably, with controlled numerics, where the doped two-dimensional Hubbard model (with and without next-nearest-neighbour hopping t′) is superconducting, striped or otherwise ordered.
Resolve the disagreement between lattice-QCD and data-driven (e+e− → hadrons) evaluations of the leading hadronic vacuum polarisation contribution to the muon anomalous magnetic moment.
Decide whether four (or seven) mutually unbiased bases exist in C^6; only three are known, and a complete set of seven is widely believed not to exist.
Explain why local distance-ladder measurements of the Hubble constant H0 disagree with the value inferred from the cosmic microwave background under ΛCDM, or show that the disagreement is systematic.
Quantum Max Cut is the quantum analog of Max Cut. Given a graph G = (E,V), it asks for the maximum eigenvalue of H_G = Σ_(ij) ∈ E (I - X_iX_j - Y_iY_j - Z_i Z_j), where X_i, Y_i, Z_i are the Pauli matrices acting on the i'th tensor factor and trivially on all other coordinates.
