aqora / Symmer-Hamiltonian
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aqora / Symmer-Hamiltonian
Original work by Kee Wang (Tufts University). This is a mirror of Kee-Wang/Symmer-Hamiltonian, generated with the symmer-pyscf pipeline and released under CC-BY-4.0. All scientific credit belongs to the original author. See Attribution & changes at the bottom of this page.
subset column:
subset | Upstream folder | What it is |
|---|---|---|
main | data/singlet/hamiltonians | 135 species in up to 5 basis sets (STO-3G, 3-21G, 6-31G**, 6-311G**, cc-pVDZ), at 10 geometry scalings |
fine_scan | data/singlet/hamiltonians_scaling_step_0d1 | 92 species on a dense grid , for smooth dissociation curves |
coulson_fisher | data/singlet/coulson_fisher_hamiltonians | 46 species whose Coulson–Fisher point lies in , sampled at |
from aqora.pyarrow import dataset
import polars as pl
data = dataset("aqora/symmer-hamiltonian", "v1.0.0")
# Metadata only: fast, skips the heavy operator columns
meta = pl.from_arrow(data.to_table(columns=["molecule_id", "basis", "alpha", "n_qubits", "n_terms", "energy_fci"]))
# One Hamiltonian, e.g. H2 / STO-3G at equilibrium
import pyarrow.compute as pc
row = data.to_table(filter=(pc.field("molecule_id") == "H2_singlet_Dooh")
& (pc.field("basis") == "sto-3g") & (pc.field("alpha") == 1.0)
& (pc.field("subset") == "main")).to_pylist()[0]
H = dict(zip(row["hamiltonian_paulis"], row["hamiltonian_coeffs"])) # {"IIII": -0.0988..., "IIZI": ..., ...}
from symmer import PauliwordOp
H_op = PauliwordOp.from_dictionary(H)
H_op.n_qubits, H_op.n_terms # (4, 15)
from qiskit.quantum_info import SparsePauliOp
# Symmer strings are qubit 0 on the left; Qiskit labels are little-endian, so reverse them
H_qk = SparsePauliOp.from_list([(p[::-1], c) for p, c in H.items()])
import numpy as np
E0 = np.linalg.eigvalsh(H_qk.to_matrix()).min()
assert abs(E0 - row["energy_fci"]) < 1e-6
number_operator, n_alpha_operator, n_beta_operator, s2_operator, uccsd_operator) are stored as the same *_paulis / *_coeffs pairs.data). Try, for example:
SELECT formula, basis, n_qubits, n_qubits_tapered, n_terms, energy_fci
FROM data WHERE subset = 'main' AND alpha = 1.0 ORDER BY n_terms DESC LIMIT 20
page_size to embed more in the static export.| Column | Type | Description |
|---|---|---|
subset | str | main, fine_scan or coulson_fisher (see above) |
source_path | str | Path of the original JSON file in the upstream repository |
molecule_id | str | {formula}_{multiplicity}_{point_group}, e.g. H2O_singlet_C2v |
formula, formula_latex | str | Chemical formula (plain / LaTeX) |
charge, multiplicity, spin | int | Net charge, (always 1), |
point_group, point_group_top | str | Point group used by PySCF / the full symmetry group |
n_atoms, n_electrons, n_alpha, n_beta | int | System size |
basis | str | Gaussian basis set |
alpha | float | Geometry scaling about the centroid (1.0 = equilibrium) |
geometry, unit | str | XYZ coordinates at this α, in Ångström |
geometry_source, geometry_from, provenance_source | str | Where the equilibrium geometry came from (CCCBDB / PennyLane / Symmer) |
qubit_encoding | str | Always JW (Jordan–Wigner) |
n_qubits | int | Qubits of the stored (untapered) operator |
n_qubits_tapered | int | Qubits after symmetry tapering |
n_terms, max_pauli_weight, mean_pauli_weight | int/float | Operator statistics (derived) |
identity_coefficient | float | Constant offset (coefficient of ) (derived) |
one_norm | float | (derived) |
hf_array | list[int8] | Hartree–Fock occupation bitstring |
hf_method, hf_method_fallback, convergence_threshold | str/float | SCF details (DIIS → level shift → Newton cascade) |
energy_hf, energy_mp2, energy_cisd, energy_ccsd, energy_fci | float | Reference energies in Hartree (null when inapplicable or not finite) |
converged_*, fci_spin_matches_target, fci_multiplicity, fci_oscillatory_converged, fci_oscillation_energy_change | bool/float | Solver diagnostics |
ccsd_t1_diagnostic | float | CCSD diagnostic (multi-reference indicator) |
alpha_coulson_fisher, coulson_fisher_status | float/str | RHF→UHF instability point for this (species, basis), from cf_summary.json |
hamiltonian_paulis, hamiltonian_coeffs | list[str], list[float] | The qubit Hamiltonian |
{number,n_alpha,n_beta,s2,uccsd}_operator_{paulis,coeffs} | list | Auxiliary operators , , , and the UCCSD generator (null when CCSD did not converge) |
generation_time_s, timestamp | float/str | Generation metadata |
b9d6bed
The Hamiltonians were generated with symmer-pyscf, building on
Symmer (UCL Centre for Computational Science) and PySCF.
Equilibrium geometries come from the NIST CCCBDB (mirror),
PennyLane molecular datasets and Symmer's reference collection. The full methodology,
data-quality report and Coulson–Fisher analysis are in the upstream
docs/ and
coulson_fisher/ folders.
Changes made for this aqora mirror. No values were recomputed. We only changed the layout:
*_paulis / *_coeffs lists.species_list*.json and Coulson–Fisher points from cf_summary.json were joined onto each row.n_terms, max_pauli_weight, mean_pauli_weight, identity_coefficient and one_norm.CCSD._t1_diagnostic_check was not carried over. See the upstream DATA_SCHEMA.md for it.@misc{wang2026symmerhamiltonian,
author = {Wang, Kee},
title = {Symmer-Hamiltonian: A curated database of molecular electronic Hamiltonians in qubit form},
year = {2026},
publisher = {GitHub},
howpublished = {\url{https://github.com/Kee-Wang/Symmer-Hamiltonian}},
note = {Tufts University. Licensed under CC-BY-4.0. Mirrored on aqora: https://aqora.io/datasets/aqora/symmer-hamiltonian}
}