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Build a quantum Hamiltonian from a molecular geometry

Source: R/quantum_nature.R
quantum_hamiltonian_from_pyscf.Rd

End-to-end ab initio pipeline:

  1. A restricted Hartree-Fock reference is computed by PySCFDriver in the requested atomic-orbital basis (STO-3G by default — minimal, illustrative, and small enough for laptop-scale VQE).

  2. Optionally, the chemical core orbitals are frozen out by FreezeCoreTransformer — a cheap and orbital-space-neutral reduction that typically halves the qubit count for first-row organics.

  3. The frontier orbitals are projected to an (num_active_electrons, num_active_orbitals) active space via ActiveSpaceTransformer, keeping the chemistry local to the coordination event the user cares about (e.g. Fe-O-C charge transfer in an organo-mineral complex).

  4. The resulting second-quantised Hamiltonian is mapped to qubits by the chosen fermion-to-qubit transformation; by default the ParityMapper is used with known particle numbers, which taper off two qubits by Z2 symmetry reduction.

Usage

quantum_hamiltonian_from_pyscf(
  atom,
  basis = "sto3g",
  charge = 0L,
  spin = 0L,
  freeze_core = TRUE,
  num_active_electrons = NULL,
  num_active_orbitals = NULL,
  mapper = c("parity", "jordan_wigner", "bravyi_kitaev")
)

Arguments

atom

Character — the PySCF atom specification, one atom per semicolon-separated block, e.g. "H 0 0 0; H 0 0 0.735" (H2 at 0.735 Angstroms) or "C 0 0 0; O 1.21 0 0; O -0.63 1.08 0; H -0.3 -0.99 0; H -1.56 0.85 0" (formic acid).

basis

Character — the atomic-orbital basis set. Default "sto3g". Use "631g", "ccpvdz", or larger for chemistry- grade accuracy at the cost of more qubits.

charge

Integer — molecular charge. Default 0.

spin

Integer — 2S, i.e. number of unpaired electrons. Default 0 (closed shell).

freeze_core

Logical — apply the frozen-core approximation before the active-space transformation. Default TRUE.

num_active_electrons

Optional integer — size of the active electron space (after freezing the core). When NULL, no active-space reduction is applied (all frontier orbitals kept).

num_active_orbitals

Optional integer — size of the active orbital space.

mapper

Character — fermion-to-qubit mapping. One of "parity" (default, with tapering by particle-number symmetry), "jordan_wigner", "bravyi_kitaev".

Value

An edaphos_quantum_hamiltonian carrying the Pauli-string Hamiltonian of the active-space problem. The object additionally exposes the following attributes:

nuclear_repulsion_energy

Nuclear-nuclear Coulomb repulsion (constant).

frozen_core_shift

Constant energy shift introduced by the frozen-core transformation (0 when freeze_core = FALSE).

reference_energy

Hartree-Fock reference energy of the active-space problem.

num_particles

Length-2 integer vector c(alpha, beta) — the number of spin-up and spin-down electrons in the active space.

num_spatial_orbitals

Number of active spatial orbitals.

geometry, basis, charge, spin, mapper

Echoed inputs.

Details

The returned object is a standard edaphos_quantum_hamiltonian and can be dropped straight into quantum_vqe_fit() or quantum_ibmq_submit(). It additionally exposes the full set of energy shifts as attributes so the user can recompute the total molecular energy from a VQE result: $$E_\mathrm{total} = \langle H \rangle_\mathrm{VQE} + E_\mathrm{shift}$$ where \(E_\mathrm{shift} = E_\mathrm{nuc} + E_\mathrm{frozen} + E_\mathrm{active}\) sums the nuclear-repulsion constant, the frozen-core shift (zero when freeze_core = FALSE) and the active-space projection shift (zero when no active-space transformation is applied). The helper quantum_nature_total_energy() performs this reconstruction on a fit object.

References

Sun, Q. et al. (2018). PySCF: the Python-based simulations of chemistry framework. WIREs Computational Molecular Science 8, e1340.

Bravyi, S. et al. (2017). Tapering off qubits to simulate fermionic Hamiltonians. arXiv:1701.08213.

See also

quantum_hamiltonian_organo_mineral_nature() for curated presets; quantum_vqe_fit() to minimise the returned Hamiltonian.

Examples

if (FALSE) { # \dontrun{
  # H2 at equilibrium bond length, 2 qubits after parity tapering:
  h2 <- quantum_hamiltonian_from_pyscf(
    atom = "H 0 0 0; H 0 0 0.735",
    basis = "sto3g", charge = 0, spin = 0
  )
  fit <- quantum_vqe_fit(h2, seed = 1L)
  fit$energy + attr(h2, "nuclear_repulsion_energy")
} # }