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1011 problems

Open problems

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.

All fields Mathematics 12Computer science 1Physics & astronomy 5Chemistry & materials 2Life sciences 2Earth & society 2
Physics 2Astrophysics & cosmology 1Quantum information 2
Source Any Curated here 2
Verification AnyA · Machine-checkableB · ReproducibleC · Reviewed Tier AnyStandardHardGrand challenges

2 shown

B Hard Quantum information

Existence of SIC-POVMs (Zauner's conjecture)

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.

0claims
0verified
B Hard Quantum information

Mutually unbiased bases in dimension 6

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.

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0verified

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