From QE and spin–orbit coupling to Qiskit

Part 3 · material to circuit

“Quantum-first” does not mean that the classical material calculation disappears. It means that every classical stage is chosen with an eventual qubit Hamiltonian, observable and hardware test in mind.

The pipeline

QE + PBE + SOC→Wannier90 spinors→fermionic H→qubit operator→Qiskit

Quantum ESPRESSO supplies relativistic Bloch states. Wannier90 turns them into localised spinor functions and hopping matrices. We then check Hermiticity, band interpolation, mode ordering and the relevant frozen windows. Only after those checks is the Hamiltonian translated into Pauli operators.

Why the order matters

An error in orbital labels or spinor ordering can produce a perfectly executable circuit that simulates the wrong physics. Material validation and circuit validation are therefore separate gates. A QPU must not become an excuse to call an untested effective Hamiltonian “gold”.

Time evolution in Qiskit

For a Pauli Hamiltonian, the evolution is the unitary U(t)=exp(−iHt). Qiskit can represent this with a PauliEvolutionGate, after which a synthesis method or product formula implements the circuit. For the 24-qubit transport observable we explicitly test whether the first-order formula is accurate enough at the selected short time.

Two routes within one project

Material-derived

The 12 modes obtained from QE+SOC/Wannier90 form the 4-qubit one-hole route. Its link to the ab-initio Hamiltonian is direct.

Au-inspired

The 24-qubit Hubbard transport model contains s–d structure, relativistic shifts, SOC and interactions, but its parameters have not yet been imported from the same Wannier calculation.

Claim boundary. The workflow is reproducible as a chain, but the present results are not yet a complete optical response of bulk gold. Screened interactions, dipole matrices across the Brillouin zone and an end-to-end error budget remain missing.

Sources and reproducibility

Project status: 8 August 2026. Numerical values come from the frozen local research artifacts; the original claim boundaries are deliberately preserved.