Open Questions

Approximability of XY

Are there any hardness of approximability results for XY analagous to the \(0.956\) barrier for QMC from [HNPTW22]?

EPR

Is finding the maximum energy of the EPR Hamiltonian easy (in \(BPP\), \(BQP\), or \(P\))? Is it \(StoqMA\)-complete? See [RT25], [MS26], and [WBGL26] for some ideas.

The singlet conjecture

For a general symmetric \(\{K\}^+\)-Hamiltonian problem, does moving a triplet state down in the energy-level ordering of local term \(K\) only make the corresponding problem easier? See Conjecture 3 of [MS26]. This would imply that \(NP=StoqMA\) and that \(EPR\) is in \(P\).