The best published ground-state energies, in one table

QMBL is a record book for variational quantum many-body simulation: one row per published energy, ranked within each Hamiltonian instance, every row citing the paper that produced the number and declaring what kind of quantity it is.

• 322Hamiltonian instances
• 813published energies
• 182instances with a record
• 67with a 2025–26 result

The frontier

The instances the field actually competes on. Energies are per site, in the convention the papers use (units and conventions). Bold is the record under the ranking rules.

○ we found no error metric in the source we read, neither an error bar nor an energy variance. † a sampled energy with a variance but no error bar. Both rows stay in the table and in rank order; the marker is a question for whoever can close it, not a criticism. See error metrics.

All 322 instances →

How current this is

67 of 322 instances carry a result published in 2025 or 2026; the rest stand where the VarBench compilation left them on 2024-10-22. Every instance page says which of the two it is, because a website that says nothing about its own currency reads as more authoritative than it is.

Separately, 31 sampled variational energies across 26 instances carry no error bar, so they are listed and rank for nothing — and 5 of them sit below their instance's current record. If one of those is your paper, the error bar is the only thing missing.

What a row claims

Every row is one published claim about one Hamiltonian instance: the energy, its error bar, the method, the primary reference, and a declared bound_type saying what the number actually is — a strict variational bound, a projected or fixed-node estimate, a zero-variance extrapolation, or a numerically exact result. Only strict variational bounds compete for a record, which is what keeps an extrapolated number from beating a measured one. The rules are in RULES.md, the row format in DATA.md.