Improved quasiparticle nuclear Hamiltonians for quantum computing

TL;DR

This paper enhances quasiparticle nuclear Hamiltonians for quantum computing by applying perturbation theory and mean-field approximations, enabling more accurate simulations of open-shell nuclei within near-term quantum device capabilities.

Contribution

It introduces a systematic method to improve quasiparticle Hamiltonians for open-shell nuclei, making them more suitable for quantum simulation.

Findings

Achieves energy errors below 0.2% compared to shell model.

Ground-state energies within 2% of exact results.

Systematic improvement over bare quasiparticle Hamiltonians.

Abstract

Quantum computing is increasingly offering concrete solutions toward the simulation of nuclear structure, with the potential to overcome the exponential scaling that limits classical diagonalization methods in large spaces. A particularly efficient encoding scheme, based on collective like-nucleon pairing modes, reduces the qubit requirements by half and avoids the non-local operator strings of standard fermion-to-qubit mappings. While this quasiparticle framework provides accurate results for semimagic nuclei, it does not adequately describe open-shell systems where proton-neutron correlations become important. In this work, we apply Brillouin-Wigner perturbation theory to systematically improve the quasiparticle description of open-shell nuclei in the $sd$ shell, reaching an energy relative error below $0.2\%$ compared to the nuclear shell model. Furthermore, to make the effective Hamiltonian suitable for quantum simulation, we introduce a mean-field Hartree-Fock approximation of the non-quasiparticle resolvent, achieving ground-state energies typically within $2\%$ of the exact shell-model result. This represents a systematic improvement over the bare quasiparticle Hamiltonian while remaining within the reach of near-term quantum devices.