Efficient pinning algorithms at the universal separability threshold
Determine whether the pinning procedures of Bakshi, Liu, Moitra, and Tang and of Putterman, Zlokapa, and Cotler provide efficient algorithms for Gibbs-state preparation up to the exact universal separability threshold z_Δ for bounded-degree Pauli Hamiltonians.
References
Our sampler does not by itself extend the temperature guarantees of the earlier pinning procedures, and it is unclear if the pinning procedures give efficient algorithms up to the threshold $z_\Delta$.
Several open questions remain. The sharpness construction allows the locality of a term to grow with $\Delta$, so the optimal constants at a fixed locality are undetermined (e.g. say $k=2$ local Hamiltonians).
Several open questions remain. The sharpness construction allows the locality of a term to grow with $\Delta$, so the optimal constants at a fixed locality are undetermined (e.g. say $k=2$ local Hamiltonians). One can also ask for thermal thresholds relative to larger classes than product states, such as convex mixtures of states prepared by shallow circuits or circuits in a fixed level of the magic hierarchy. Finally, random Hamiltonians may have typical thresholds different from the worst-case bound.