Researchers propose a practical way to make a compact encoding of atomic nuclei more accurate for quantum simulation. They start from a “quasiparticle” picture that encodes paired nucleons (protons and neutrons) into qubits. Then they use Brillouin–Wigner perturbation theory to fold the effect of excitations outside that paired space back into an improved effective Hamiltonian. The result is a much better description of open‑shell nuclei while keeping the advantages of the compact encoding.

Concretely, the authors test their approach in the sd shell of nuclear states. They use the standard USDB shell‑model interaction and show that the Brillouin–Wigner (BW) correction reduces energy errors to below 0.2% relative to the full nuclear shell model. To make the correction practical for near‑term devices, they also replace the correlated propagator outside the quasiparticle space with a Hartree–Fock (HF) mean‑field approximation. That HF‑BW variant typically yields ground‑state energies within about 2% of the exact shell‑model result.

At a high level the method builds on a pairing encoding. Each qubit represents a paired mode that creates two nucleons in time‑reversed single‑particle orbitals. This halves the number of qubits compared to a direct fermion encoding. The pair operators obey a ‘‘hardcore boson’’ algebra that maps to local single‑qubit Pauli operators. That avoids the long Pauli strings that appear in standard fermion‑to‑qubit maps and makes the Hamiltonian local and simpler to implement on hardware.

Brillouin–Wigner perturbation theory then treats states outside the paired (quasiparticle) model space as virtual excitations. Their influence is incorporated into an energy‑dependent effective Hamiltonian that acts only on the compact quasiparticle space. The HF approximation replaces the fully correlated propagator of the excluded states with one built from a simple Hartree–Fock reference state. This lowers classical preprocessing cost and preserves the local qubit structure needed for near‑term quantum devices.