Toy organo-mineral Hamiltonian (4-qubit Fe + ligand coupling) — quantum_hamiltonian_organo

A deliberately minimalist representation of a clay-humus or iron- oxide coordination complex, sized for classical simulation on a laptop and for a meaningful walk-through of quantum_vqe_fit() in the Pillar 6 vignette. Four qubits are partitioned as two metal-centre states (left pair) and two ligand states (right pair), with on-site, same-sector exchange and cross-sector hopping / tunnelling terms:

Usage

quantum_hamiltonian_organo_mineral(
  eps_fe = 0.5,
  eps_l = 0.3,
  j_fe = 0.4,
  j_l = 0.2,
  t = 0.25
)

Arguments

eps_fe, eps_l: Numeric on-site energies for the Fe-like and ligand-like sub-sectors.
j_fe, j_l: Numeric same-sector Z-Z exchange couplings.
t: Numeric cross-sector X-X hopping amplitude.

Value

An edaphos_quantum_hamiltonian with 4 qubits.

Details

$$ H = -\,\varepsilon_\mathrm{Fe}\,(Z_3 + Z_2) \; -\,\varepsilon_\mathrm{L}\,(Z_1 + Z_0) \; +\,J_\mathrm{Fe}\,Z_3 Z_2 \; +\,J_\mathrm{L}\,Z_1 Z_0 \; +\,t\,(X_3 X_0 + X_2 X_1). $$

The default parameters $(\varepsilon_\mathrm{Fe}, \varepsilon_\mathrm{L}, J_\mathrm{Fe}, J_\mathrm{L}, t) = (0.5, 0.3, 0.4, 0.2, 0.25)$ give a non-trivial entangled ground state.