Chemically decisive benchmarks on the path to quantum utility

TL;DR

The paper addresses the need for chemically meaningful benchmarks to drive quantum-chemistry algorithm development in the near term. It introduces a curated hierarchy of benchmark systems—N$_2$, FeS, [2Fe–2S], and U$_2$—that span distinct electronic-correlation regimes, paired with a practical black-box workflow combining automated active-space selection (ActiveSpaceFinder) and the ADAPT-GCIM adaptive subspace algorithm. Across these systems, ADAPT-GCIM achieves high accuracy, while the results also reveal general failure modes tied to operator-pool design and symmetry constraints, underscoring the necessity of problem-aware, correlation-specific strategies. The authors openly share the Hamiltonians to enable reproducible benchmarking and provide a scalable framework for evaluating current and future quantum algorithms as hardware advances toward quantum utility in chemistry.

Abstract

Progress towards quantum utility in chemistry requires not only algorithmic advances, but also the identification of chemically meaningful problems whose electronic structure fundamentally challenges classical methods. Here, we introduce a curated hierarchy of chemically decisive benchmark systems designed to probe distinct regimes of electronic correlation relevant to molecular, bioinorganic, and heavy-element chemistry. Moving beyond minimal toy models, our benchmark set spans multireference bond breaking (N$_2$), high-spin transition-metal chemistry (FeS), biologically relevant iron-sulfur clusters ([2Fe-2S]), and actinide-actinide bonding (U$_2$), which exhibits extreme sensitivity to active-space choice, relativistic treatment, and correlation hierarchy even within advanced multireference frameworks. As a concrete realization, we benchmark a recently developed automated and adaptive quantum algorithm based on generator-coordinate-inspired subspace expansion,ADAPT-GCIM, using a black-box workflow that integrates entropy-based active-space selection via the ActiveSpaceFinder tool. Across this chemically diverse problem set, ADAPT-GCIM achieves high accuracy in challenging correlation regimes. Equally importantly, these benchmarks expose general failure modes and design constraints-independent of any specific algorithm-highlighting the necessity of problem-aware and correlation-specific strategies for treating strongly correlated chemistry on quantum computers. To support systematic benchmarking and reproducible comparisons, the Hamiltonians for all systems studied are made openly available.

Figures (9)

• Figure 1: Comparison of ground state energy and error analysis for the $\mathrm{N_2}$ system. (a) ADAPT-GCIM ground-state energies compared with CASCI. The dashed gray line denotes the CASCI reference. (b) Comparison of errors $E_{\mathrm{ADAPT-GCIM}} - E_{\mathrm{CASCI}}$ over entire bond distances. The shaded region below the dashed gray line indicates "chemical accuracy" as 1.59 $\times 10^{-3}$ Ha(1 kcal/mol).
• Figure 2: FeS benchmark using ADAPT-GCIM with a quintet reference state. (a) Potential energy surface comparing ADAPT-GCIM and CASCI energies within the (6e,6o) active space using the ANO-RCC-MB basis. (b) Corresponding energy errors $E_{\mathrm{ADAPT-GCIM}} - E_{\mathrm{CASCI}}$ across the Fe--S bond dissociation coordinate. The dashed grey line indicates chemical accuracy (1.59$\times10^{-3}$ Ha).
• Figure 3: Potential energy surface and accuracy analysis for $\mathrm{U_2}$ in the (6e,6o) active space with a spin-free X2C-1e Hamiltonian and ANO-RCC-MB basis. (a) Ground-state potential energy surface obtained from ADAPT-GCIM using SingletSD and SingletGSD operator pools, compared against CASCI reference energies. (b) Corresponding energy errors $E_{\mathrm{ADAPT\text{-}GCIM}} - E_{\mathrm{CASCI}}$ along the dissociation coordinate. The dashed grey line indicates chemical accuracy (1.59 $\times 10^{-3}$ Ha). SingletGSD achieves substantially improved accuracy by enhancing connectivity within the singlet manifold.
• Figure 4: Comparison of ADAPT-GCIM convergence for $\mathrm{U_2}$ using SingletSD alone and SingletSD augmented with specific classes of generalized doubles. Inclusion of T4-type generalized singles and doubles, which directly couple electrons between different spatial orbitals, enables convergence to chemical accuracy with significantly fewer operators. This highlights the critical role of operator-pool design in efficiently capturing strong multireference correlation. Each line in the plot stops when the operators in the pool are exhausted.
• Figure 5: Total probability of n-body excited determinants, comparing CASCI, (ADAPT‑GCIM SingletSD) and (ADAPT-GCIM-SingletSD)$^5$ wavefunctions as a function of excitation rank. Determinants are grouped by excitation rank relative to the reference Hartree-Fock configuration, and the total probability is accumulated for each excitation order.