QB-GSEE Benchmark Repository

• The QB-GSEE Benchmark Repository is an openly available framework offering standardized benchmarks for ground state energy estimation across diverse quantum chemistry and condensed matter physics instances.
• It integrates classical methods like SHCI and DMRG with quantum approaches such as DF QPE by using consistent instance formats, shared FCIDUMP integrals, and unified performance metrics.
• The repository emphasizes reproducibility and comparability through structured schemas, machine learning-based solvability analysis, and transparent evaluations of accuracy, runtime, and scalability.

The QB-GSEE Benchmark Repository is an openly available repository and benchmarking framework for Ground State Energy Estimation (GSEE), intended to support systematic comparison of classical and quantum solvers on diverse problem instances in quantum chemistry and condensed matter physics. In the benchmark formulation, GSEE is the task of finding the lowest eigenvalue of a many-body Hamiltonian, with the variational principle written as $$E_0 = \min_{|\psi\rangle} \langle \psi|H|\psi\rangle / \langle \psi|\psi\rangle$$, and with standard electronic-structure instances represented in second quantization as $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$. The repository integrates fermionic and qubit features, common instance formats such as FCIDUMP, solver configurations, and machine-learning-based solvability analysis to make accuracy, reliability, runtime, and scaling trade-offs comparable across methods (Bellonzi et al., 14 Aug 2025).

1. Scientific context and problem formulation

Ground State Energy Estimation is presented as a foundational computational task because the lowest eigenvalue of a many-body Hamiltonian underlies reaction thermochemistry, phase stability, catalysis, and electronic properties of molecules and materials. Exact diagonalization scales combinatorially in the number of spin-orbitals $N$ and electrons $\eta$, so practical methods rely on structure and approximation, including reduced determinant expansions, tensor networks, and coupled-cluster approximations on the classical side, and phase estimation with block encodings, qubitization, and state preparation on the quantum side (Bellonzi et al., 14 Aug 2025).

The benchmark takes a principled stance on GSEE as a promise problem. It assumes an “easy-to-prepare” initial state $\rho$ with overlap $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$ and a gap $\Delta = \epsilon_1 - \epsilon_0 \ge \Delta_0$, and seeks an estimate of $E_0$ within accuracy $\gamma$ and with failure probability less than $\delta$. This framing turns solver comparisons into explicit measurements of accuracy, success probability, and time-to-solution rather than informal comparisons across incompatible instances or resource models.

A standardized repository is motivated by three stated concerns. Hamiltonians differ widely in correlation, sparsity, and entanglement; recent quantum resource estimates depend sensitively on encoding choices, one-norm bounds, state overlaps, and error budgets; and real-world utility depends on end-to-end time-to-solution with validated accuracy rather than isolated subroutines or toy examples. A plausible implication is that the repository is designed not merely as a dataset archive but as a normalization layer for evaluation methodology.

2. Repository contents, instance coverage, and data organization

The benchmark spans molecular systems, condensed-matter models, and utility-oriented instances. Molecular systems include diatomics such as $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$0 and $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$1, small and medium organics such as propane $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$2 and benzene, transition-metal dimers such as $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$3, and ozone at multiple geometries. Condensed-matter coverage includes Fermi-Hubbard and Heisenberg models. The repository also includes utility-oriented and planted instances, including homogeneous catalysis, corrosion modeling, protein interaction fragments, and planted-solution Hamiltonians with exactly known references (Bellonzi et al., 14 Aug 2025).

Basis sets and active spaces are encoded via FCIDUMP, and the benchmark emphasizes consistent FCIDUMP integrals to avoid solver bias introduced by internal integral generation. Curation distinguishes between benchmark instances, which have trusted references that are often FCI-quality or arise from agreement between fundamentally different solvers, and guidestar instances, which are important but sometimes intractable to current classical methods.

The repository structure is described explicitly in terms of directories, schemas, and file formats.

Repository component	Contents
problem_instances/ or data/	FCIDUMP files, metadata, instance descriptors in JSON/YAML
features/	Scripts and notebooks for fermionic and qubit features
performers/solvers/	Configurations for SHCI, DMRG, and DF QPE
reports/	Standard Report assets, including solvability maps and SHAP analyses
examples/	End-to-end notebooks such as examples/run_dmrg.ipynb
schema/	Problem and solution schemas with validation utilities

The repository uses FCIDUMP for integrals; JSON or YAML for instances and solver runs; and CSV or JSON for features and results. Solution files conform to a schema containing energies, runtime, memory, parameters, and status flags. Schema validation is used to ensure consistency of instance and solution files, and versioning is handled through Git tags and releases. The repository is openly available at https://github.com/isi-usc-edu/qb-gsee-benchmark (Bellonzi et al., 14 Aug 2025).

3. Double-factorization, solver classes, and evaluation metrics

A central representational choice is double-factorization (DF) of the two-electron interaction tensor. The benchmark uses the form

$$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$4

where $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$5 is the DF rank and the $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$6 and $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$7 terms summarize fragment weights and structure. DF rank and the DF eigenvalue spectrum are treated as features indicative of interaction complexity and expected simulation cost. The repository also computes qubit-side features such as the one-norm $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$8, Pauli-string count $$H = \sum_{pq} h_{pq} a_p^{\dagger} a_q + (1/2)\sum_{pqrs} g_{pqrs} a_p^{\dagger} a_q^{\dagger} a_r a_s$$9, and hypergraph statistics (Bellonzi et al., 14 Aug 2025).

The Standard Report currently tracks 21 solvers, while the paper centers on three representative methods: SHCI, DMRG, and DF QPE. SHCI uses heat-bath-guided determinant selection, a variational energy from the selected subspace, semistochastic PT2 correction, and extrapolation toward the FCI limit. The selection condition is given as $N$0, and the PT2 correction is

$N$1

The benchmark considers $N$2, along with presence or absence of PT2 and orbital optimization.

DMRG is treated as variational optimization in the matrix product state manifold. Its energy functional is $N$3, with bond dimension $N$4 and truncation controlled by discarded weight or singular-value thresholds. Entanglement is characterized by the von Neumann entropy $N$5. The benchmark uses starting $N$6, automatic 10% increments, a stopping criterion of convergence within $N$7 or a 23.5-hour limit, adaptive numbers of sweeps, and optimized orbital ordering.

DF QPE uses qubitized Quantum Phase Estimation with DF block encoding. The reported implementation uses pyLIQTR, qualtran, and OpenFermion; a fixed DF truncation threshold of $N$8; the dominant Configuration State Function as the initial state; and an overlap estimate $N$9 from block2 DMRG. The target is chemical accuracy of $\eta$0 with 99% success probability accounting for finite overlap, algorithmic failure, hardware failure, and phase estimation parameters. Logical runtime scales roughly as $\eta$1 up to polylogarithmic factors, where $\eta$2 is determined by the chosen encoding and grouping.

The benchmark methodology evaluates solvers by accuracy, efficiency, and scalability. Accuracy is measured through absolute energy error $\eta$3, fraction of correlation energy recovered, and whether chemical-accuracy thresholds are met. Efficiency is measured through wall-clock runtime, memory footprint, and a solvability ratio defined from a machine-learning-estimated probability of at least 0.5 across a latent feature space rather than as a raw solved/attempted fraction. Scalability is analyzed against $\eta$4, $\eta$5, $\eta$6 FCI dimension, DF rank $\eta$7, and qubit features.

4. Reported results and interpretation

The reported benchmark outcome is that fully optimized SHCI achieves near-universal solvability on the tested instances, DMRG performs strongly in low-entanglement regimes, and DF QPE remains constrained by current hardware and algorithmic assumptions (Bellonzi et al., 14 Aug 2025). The repository’s solvability analyses are based on latent-space models constructed with PCA or NNMF and on SVM classifiers trained on solved/unsolved labels, with SHAP analyses used to rank feature importance. The paper states that DF eigenvalue gap, electrons $\eta$8, orbitals $\eta$9, and $\rho$0 FCI dimension often dominate these analyses.

The quantitative summary in the Standard Report distinguishes clearly between latent-space solvability and raw task counts.

Solver/configuration	Reported solvability	Additional reported count
SHCI Opt	1.0000	148 of 226 attempted tasks
SHCI, $\rho$1	$\rho$2	not separately summarized here
SHCI, $\rho$3	$\rho$4	not separately summarized here
SHCI, $\rho$5	$\rho$6	not separately summarized here
DMRG, lowest variational energy within a 24-hour profile	$\rho$7	107 of 228 tasks solved
DF QPE	$\rho$8	4 of 131 tasks “solved”

Several interpretive cautions are explicit. First, the solvability ratio is not simply the fraction of solved tasks among attempted tasks; it is derived from ML-estimated probability over a latent feature space. Second, the paper notes that the DMRG “first run” definition, taken as the lowest variational energy within a 24-hour budget, does not represent best-possible DMRG, because extrapolated or higher-$\rho$9 settings could improve accuracy. Third, the DF QPE count of 4 of 131 tasks “solved” refers to feasibility under a hardware model and runtime threshold rather than to verification against reference energies.

The paper also identifies conditions under which quantum methods may become more favorable. It points to large, delocalized, highly correlated systems where DF or THC yields favorable rank and symmetry structure, and where MPS state preparation can improve overlap $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$0. Suggested improvements include THC block encodings, BLISS symmetry shifts, and better state preparation such as MPS-based approaches. This suggests that the repository is intended to track regime changes in comparative advantage rather than to provide a fixed ranking of solver paradigms.

5. Reproducibility, fairness controls, and workflow

The repository is explicitly organized around reproducibility and fairness. Fairness controls include shared FCIDUMP integrals, consistent active spaces and spin symmetries, documented solver versions and configurations, controlled random seeds, unified convergence thresholds where applicable, and common runtime budgets (Bellonzi et al., 14 Aug 2025). Reference solutions are taken either from literature FCI-level references or from agreement between fundamentally different algorithms such as SHCI and DMRG within half-chemical-accuracy. A plausible implication is that the repository treats cross-method agreement as a practical standard for trustworthy reference energies when exact solutions are unavailable.

Reproducibility is supported through structured problem schemas, deterministic pipelines, notebook- and script-based runs, tracked environment dependencies, and solvability ML models with cross-validation. Installation is described in practical terms: the repository can be cloned from GitHub, Python dependencies are installed through requirements.txt, SHCI and DMRG tools such as block2 require separate installation, and pyLIQTR, qualtran, and OpenFermion support the quantum resource-estimation path. Some instances require credentials for data retrieval through an sftp server noted in the examples.

The workflow for adding instances and solvers is also standardized. New instances require an FCIDUMP and an instance JSON conforming to schema, including metadata such as basis, spin, electrons, orbitals, and reference availability. New solvers are integrated by generating solution files with energies, runtime, memory, parameters, and status flags, plus a solver UUID and short name. Feature computation, ML-pipeline updates, and report regeneration then place the new results into the same latent-space and report infrastructure as existing solvers.

This emphasis on common artifacts, shared metadata, and result sharing is aligned with a broader benchmark-repository rationale in empirical software engineering, where curated shared artifacts are proposed to improve fairness, reproducibility, and comparability across studies (Sulír, 2020).

6. Biases, limitations, and future development

A central limitation identified in the benchmark is dataset bias. The paper states that many benchmark Hamiltonians are drawn from datasets tailored to SHCI and related approaches, which introduces a bias favoring classical determinant-selection schemes and perturbative corrections. It further states that this bias inflates SHCI’s apparent universality compared to tensor-network and quantum approaches (Bellonzi et al., 14 Aug 2025).

The repository roadmap addresses this bias by proposing strongly correlated, multireference, and extended-delocalization systems that stress SHCI and may reward DMRG or quantum methods; more lattice models with tunable entanglement and sign issues; and larger industrial catalysis instances, including planted solutions with exact references. It also proposes clearer criteria for new instances, including availability of integrals in FCIDUMP, metadata completeness, consistent schema, target accuracy, and a plan for reference determination.

Methodological limitations are also explicit on the quantum side. DF QPE feasibility is sensitive to hardware model choices, including surface-code cycle time, physical error rate, serial versus shot-parallel execution, and distillation assumptions such as catalyzed AutoCCZ factories. The repository therefore requires hardware-model assumptions, overlap estimates, and error budgets to be reported clearly. The total QPE error budget is decomposed into $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$1, $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$2, $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$3, $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$4, and $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$5, with the repository reports targeting $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$6 at 99% success and assuming that DF truncation at $\xi = \langle \psi_0|\rho|\psi_0\rangle \ge \xi_0$7 incurs negligible error in large systems.

The future direction is not described as replacing classical methods, but as maintaining a scalable and open resource for tracking comparative progress. As cycle times and error rates improve, and as algorithmic innovations such as BLISS and better state preparation are incorporated, the repository is intended to provide a forward-looking basis for identifying domains in which quantum methods may eventually surpass classical solvers.