Researchers report that a class of hard electronic-structure problems once highlighted as promising targets for quantum computers can be solved to very high accuracy on modern classical hardware. Using an advanced classical algorithm called Density Matrix Renormalization Group (DMRG) together with graphics processing units (GPUs), the team produced benchmark results for iron–sulfur molecular clusters that are often described as “multi‑reference” and difficult for standard methods.

The group focused on an Fe4S4 cluster in a so‑called complete active space of 54 electrons in 36 orbitals, written CAS(54,36). A version of this problem appears on the Quantum Advantage Tracker maintained by IBM and RIKEN as a candidate for quantum speedup. The authors used spin‑adapted, mixed‑precision DMRG calculations interfaced to the ORCA quantum chemistry package and ran them on NVIDIA Blackwell GPUs. They also performed orbital optimizations using the complete active space self‑consistent field (CAS‑SCF) approach for much larger active spaces, including up to CAS(89,102) and even mention active spaces with hundreds of electrons and orbitals for a related Fe5S12H4^{5−} system.

At a high level, DMRG represents the quantum state as a compressed object called a matrix product state (MPS). A single control parameter, the bond dimension (denoted D), sets how much detail the representation can capture: larger D gives more accurate results but costs more memory and time. The authors ran calculations with symmetry‑adapted multiplets up to DSU(2)=12,280 and used systematic extrapolations to estimate the energy one would get with infinitely large D. For the Fe4S4 CAS(54,36) model they report extrapolated ground‑state energies around −327.247 hartree; two independent extrapolation procedures differed by about 0.2 milli‑hartree (0.0002 hartree), which gives a sense of the residual uncertainty.