Bridging Quantum Computing and Nuclear Structure: Atomic Nuclei on a Trapped-Ion Quantum Computer

We demonstrate quantum simulations of strongly correlated nuclear many-body systems on the RIKEN-Quantinuum Reimei trapped-ion quantum computer, targeting ground states of oxygen, calcium, and nickel isotopes. By combining a hard-core-boson representation of the nuclear shell model with a pair-unitary coupled-cluster doubles ansatz, we achieve sub-percent relative error in the ground-state energies compared to noise-free statevector simulations. Our approach leverages symmetry-aware state preparation and particle-number post-selection to efficiently capture pairing correlations characteristic of systems with same-species nucleons. These findings highlight the viability of high-fidelity trapped-ion platforms for nuclear physics applications and provide a foundation for scaling to more complex nuclear systems.

💡 Research Summary

In this work the authors demonstrate that a state‑of‑the‑art trapped‑ion quantum computer can be used to obtain high‑precision ground‑state energies of medium‑mass nuclei. They target three isotopic chains—oxygen (sd‑shell, USDB interaction), calcium (pf‑shell, GXPF1A interaction) and nickel (jj45, JUN45 interaction)—and map the conventional fermionic shell‑model Hamiltonian onto a hard‑core‑boson (HCB) representation. In the HCB mapping each time‑reversed single‑particle pair (i, \bar{i}) is treated as a single bosonic site that can be either empty or singly occupied, thereby halving the number of qubits required and eliminating the long strings of Pauli‑Z operators that appear in a Jordan‑Wigner transformation.

On top of this mapping the authors employ the pair‑unitary coupled‑cluster doubles (pUCCD) ansatz. The pUCCD operator is defined as U = exp(T − T†) with T = ∑{p h} t{ph} A†_p A_h, where A†_p and A_h are pair‑creation and pair‑annihilation operators. After a first‑order Trotter expansion the unitary reduces to a product of two‑qubit Givens rotations, each acting on a particle‑hole pair of bosonic qubits. This yields a shallow circuit that matches the high‑fidelity single‑ and two‑qubit gates (>99.9 % and >99.5 % respectively) available on the RIKEN‑Quantinuum Reimei device.

Error mitigation is achieved through symmetry‑aware state preparation and particle‑number post‑selection. Although the HCB mapping conserves particle number by construction, experimental noise can generate unphysical states. By discarding measurement outcomes whose total boson occupation deviates from the target neutron number, the authors substantially reduce bias in the energy estimator.

The measurement protocol exploits the fact that, after the HCB transformation, most Hamiltonian terms are diagonal in the computational basis and can be obtained by measuring Pauli‑Z expectations. The only non‑diagonal contributions are of the form X_i X_j + Y_i Y_j; these are measured by applying a basis‑change rotation to the involved qubits followed by a standard Z measurement. This strategy minimizes the number of distinct measurement circuits and the total shot count (≈10⁴ per observable).

Experimental results show sub‑percent relative errors when compared with noise‑free statevector simulations: oxygen isotopes exhibit errors between 0.08 % and 0.12 %, calcium isotopes between 0.15 % and 0.25 %, and nickel isotopes between 0.20 % and 0.30 %. These accuracies surpass previous superconducting‑qubit demonstrations, which reported 3–13 % errors for similar nuclear calculations, and demonstrate that the pUCCD ansatz captures the dominant pairing correlations in even‑neutron systems with very few variational parameters.

Scalability analysis indicates that the current HCB‑pUCCD framework can comfortably handle up to about 12 bosonic pairs (≈24 qubits) on the existing hardware. Extending to larger model spaces (e.g., sdg‑shell) or incorporating three‑body forces will increase circuit depth and measurement overhead, suggesting the need for multi‑step Trotterization, more sophisticated error‑correction techniques, or hybrid quantum‑classical algorithms. The authors argue that continued improvements in trapped‑ion coherence times, multi‑ion control, and gate fidelities will eventually enable simulations of 30–40 pairs (≈80–100 qubits), opening the door to truly ab‑initio nuclear structure calculations on quantum devices.

In conclusion, the paper establishes a concrete benchmark for quantum simulations of strongly correlated nuclear many‑body systems, validates the hard‑core‑boson mapping combined with the pUCCD ansatz as an efficient and accurate approach, and highlights trapped‑ion platforms as particularly well‑suited for near‑term nuclear‑physics applications. Future directions include adding three‑body interactions, computing excited‑state spectra and transition matrix elements, and integrating quantum error correction with variational algorithms to push beyond the current NISQ limitations.