This paper reports that highly optimized classical calculations can reach very high accuracy on a long‑standing hard problem in quantum chemistry. The authors used advanced tensor‑network methods on modern graphics processors to compute the ground‑state energy and orbital behavior of an iron–sulfur cluster that has been proposed as a candidate for showing a future quantum computer advantage. Their results show that classical methods remain a strong reference point when comparing to quantum hardware.

At a high level they used the Density Matrix Renormalization Group (DMRG), a tensor‑network algorithm that represents the quantum wavefunction in a compressed form. DMRG accuracy is controlled by a parameter called the bond dimension (D) or, in their spin‑adapted implementation, the number of SU(2) multiplets DSU(2). The team ran mixed‑precision, spin‑adapted ab initio DMRG coupled to the ORCA quantum chemistry package and pushed performance on NVIDIA’s Blackwell GPU platform. They report careful convergence criteria: energy sweeps were continued until the energy change across sweeps fell below 10^−5 and the iterative Lanczos solver had a residual of 10^−6.

Their main target was the Fe4S4 molecular cluster in a CAS(54,36) model space — that means 54 correlated electrons in 36 orbitals, a setup known to be “multi‑reference” or strongly correlated. The authors show an orbital occupation profile that makes clear many orbitals are neither nearly full nor empty, which is what makes the problem hard for simple mean‑field methods. They performed DMRG calculations up to DSU(2)≈12280 multiplets, extrapolated the energy to the truncation‑free limit by two different procedures, and obtained extrapolated ground‑state energies of −327.2471 Hartree and −327.2469 Hartree. The difference between those two extrapolations is 0.2 milliHartree, which gives a sense of the remaining numerical uncertainty.