Quantum chemistry datasets

Quantum chemistry is one of the most promising directions for research in quantum algorithms. Here you can explore our available quantum chemistry datasets for some common molecular systems.

Molecules

We provide the electronic structure data for 42 different geometries of the following molecules:

  • Linear hydrogen chains: H2, H4, H6, H8.
  • Metallic and non-metallic hydrides: - LiH, BeH2, BH3, NH3, H2O, HF.
  • Charged species: HeH+, H3+, OH-.

For the smaller molecules such as H2, HeH+, and H3+, data has been obtained for both the minimal basis-set STO-3G and the split-valence double-zeta basis set 6-31G. For the remaining molecules, data is only available for the former basis-set. The geometries for each molecule are defined by the bond lengths between atoms, with the available bondlengths given as 41 equally spaced values within a range (see the table below). In addition to these, we also include data for the optimal ground-state geometry of each molecule. We summarise all of this information for all the molecules in the table below.

Accessing chemistry datasets

The quantum chemistry datasets can be downloaded and loaded to memory using the load() function as follows:

>>> data = qml.data.load("qchem", molname="H2", basis="STO-3G", bondlength=1.1)[0]
>>> print(data)
<Dataset = description: qchem/H2/STO-3G/1.1, attributes: ['molecule', 'hamiltonian', ...]>

Here, the positional argument "qchem" denotes that we are loading a chemistry dataset, while the keyword arguments molname, basis, lattice, and bondlength specify the requested dataset. The possible values for these keyword arguments are included in the table below. For more information on using PennyLane functions please see the PennyLane Documentation.

Molecule Basis set(s) #Qubits Bond length (Å), Bond angle (°) Optimal geometry (Å, °)
H2 STO-3G / 6-31G 4 / 8 H𝐴−H𝐵 ∈ [0.5,2.1] Å H𝐴−H𝐵 = 0.742 Å
HeH+ STO-3G / 6-31G 4 / 8 He−H ∈ [0.5,2.1] Å He−H= 0.775 Å
H+3 STO-3G / 6-31G 6 / 12 H𝐴−H𝐵 ∈ [0.5,2.1] Å, ∡ HHH = 60° H𝐴−H𝐵 = 0.874 Å, ∡ HHH = 60°
H4 STO-3G 8 H𝐴−H𝐵 ∈ [0.5,1.3] Å, ∡ HHH = 180° N/A
LiH STO-3G 12 Li−H ∈ [0.9,2.1] Å Li−H = 1.57 Å
HF STO-3G 12 H−F ∈ [0.5,2.1] Å H−F = 0.917 Å
OH- STO-3G 12 O−H ∈ [0.5,2.1] Å O−H = 0.964 Å
H6 STO-3G 12 H𝐴−H𝐵 ∈ [0.5,1.3] Å, ∡ HHH = 180° N/A
BeH2 STO-3G 14 Be−H ∈ [0.5,2.1] Å, ∡ HBeH = 180° Be−H = 1.33 Å, ∡ HBeH = 180°
H2O STO-3G 14 H−O ∈ [0.5,2.1] Å, ∡ HOH = 104.5° H−O = 0.958 Å, ∡ HOH = 104.5°
H8 STO-3G 16 H𝐴−H𝐵 ∈ [0.5,0.9] Å, ∡ HHH =180° N/A
BH3 STO-3G 16 B−H ∈ [0.5,2.1] Å, ∡ HBH = 120° B−H = 1.189 Å, ∡ HBH = 120°
NH3 STO-3G 16 N−H ∈ [0.5,2.1] Å, ∡ HNH =106.8° N−H = 1.11 Å, ∡ HNH = 106.8°

Data features

For each of the molecules mentioned above, the following characteristics can be extracted for each geometry:

Molecular data

Information regarding the molecule, including its complete classical description and the Hartree Fock state.

Name Type Description
molecule Molecule PennyLane Molecule object containing description for the system and basis set
hf_state numpy.ndarray Hartree-Fock state of the chemical system represented by a binary vector

Hamiltonian data

Hamiltonian for the molecular system under Jordan-Wigner transformation and its properties.

Name Type Description
hamiltonian Hamiltonian Hamiltonian of the system in the Pauli basis
sparse_hamiltonian scipy.sparse.csr_array Sparse matrix representation of a Hamiltonian in the computational basis
meas_groupings list[list[list[Operator]], list[tensor_like]] List of grouped qubit-wise commuting Hamiltonian terms
fci_energy float Ground state energy of the molecule obtained from exact diagonalization
fci_spectrum numpy.ndarray First 2×
#qubits eigenvalues obtained from exact diagonalization

Auxiliary observables

The supplementary operators required to obtain additional properties of the molecule such as its dipole moment, spin, etc.

Name Type Description
dipole_op Hamiltonian Qubit dipole moment operators for the chemical system
number_op Hamiltonian Qubit particle number operator for the chemical system
spin2_op Hamiltonian Qubit operator for computing total spin 𝑆2 for the chemical system
spinz_op Hamiltonian Qubit operator for computing total spin’s projection in 𝑍 direction

Tapering data

Features based on 𝑍2 symmetries of the molecular Hamiltonian for performing tapering.

Name Type Description
symmetries list[Hamiltonian] Symmetries required for tapering molecular Hamiltonian
paulix_ops list[PauliX] Supporting PauliX ops required to build Clifford 𝑈 for tapering
optimal_sector numpy.ndarray Eigensector of the tapered qubits that would contain the ground state

Tapered observables data

Tapered observables and Hartree-Fock state based on the on 𝑍2 symmetries of the molecular Hamiltonian.

Name Type Description
tapered_hamiltonian Hamiltonian Tapered Hamiltonian
tapered_hf_state numpy.ndarray Tapered Hartree-Fock state of the molecule
tapered_dipole_op Hamiltonian Tapered dipole moment operator
tapered_num_op Hamiltonian Tapered number operator
tapered_spin2_op Hamiltonian Tapered total spin operator
tapered_spinz_op Hamiltonian Tapered spin projection operator

VQE data

Variational data obtained by using AdaptiveOptimizer to minimize ground state energy.

Name Type Description
vqe_gates list[Operation] SingleExcitation and DoubleExcitation gates for the optimized circuit
vqe_params numpy.ndarray Optimal parameters for the gates that prepares ground state
vqe_energy float Energy obtained from the state prepared by the optimized circuit

Contents