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

TL;DR

This work demonstrates accurate quantum simulations of strongly correlated nuclear systems on a trapped-ion quantum computer by marrying a hard-core-boson mapping of the shell model with a compact pair-unitary coupled-cluster doubles (pUCCD) ansatz. The method efficiently captures pairing correlations and uses symmetry-aware state preparation and particle-number post-selection to evaluate energies, achieving sub-percent agreement with noise-free simulations for oxygen, calcium, and nickel isotopes and high-fidelity hardware results on the Reimei device. Hardware measurements, particularly with the basis-rotation measurement strategy for XX+YY terms, show energies within ~0.3% of ideal pUCCD and illustrate the practicality of near-term trapped-ion platforms for nuclear-structure calculations. Overall, the study provides a scalable, physically motivated pathway toward larger and more complex nuclear systems, with open data and clear avenues for extending to non-pair correlations and proton-neutron interactions.

Abstract

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.

Figures (7)

• Figure 1: Schematics of the hard-core boson (HCB) representation. This example shows a configuration of ${}^{22}$O nucleus on top of the inert core ${}^{16}$O. The active (valence) space consists of $1s_{1/2}, 0d_{3/2}$, and $0d_{5/2}$ single-particle states.
• Figure 2: Sketched quantum circuits for preparing the pUCCD ansatz taking ${}^{22}$O as an example. Original single-particle states in the $sd$ shell consist of twelve states for neutrons, which are now represented by six qubits in the HCB representation. (a) Circuit layout suitable for devices with heavy-hexagon connectivity. (b) Circuit layout for all-to-all connectivity. First, the reference state is prepared by applying $X$ gates to qubits. Then, Givens rotations are applied to take into account particle-hole excitations of nucleon pairs. Single-qubit rotations are applied as needed prior to measuring Hamiltonian expectation values.
• Figure 3: Ground-state energies of target isotopes on noise-free statevector simulators. (a)--(c) Ground-state energies of oxygen, calcium, and nickel isotopes, respectively. Full configuration interaction (FCI, dotted lines with gray circles) and doubly occupied configuration interaction (DOCI, blue diamonds) are compared with statevector simulations using the pUCCD(GS) ansatz (green stars) and the pUCCD(G) ansatz (red triangles). (d)--(f) Differences between the pUCCD ansatz results and the DOCI results are shown relative to FCI in logarithmic scale. Uncertainty bands for pUCCD(G) are obtained by random sampling over circuits with different initial configurations and Givens-rotation orderings.
• Figure 4: Relative errors in ground-state energies on the RIKEN-Quantinuum Reimei device. The results are shown for oxygen (a), calcium (b), and nickel (c) isotopes, using two measurement strategies: Hadamard and basis rotation. The error bars represent 1 $\sigma$ statistical uncertainties evaluated by bootstrapping, and the shaded band corresponds to a $0.3\%$ error.
• Figure 5: Bootstrapping of hardware results for ${}^{66}\mathrm{Ni}$. (a) diagonal terms. (b) $XX+YY$ terms evaluated by two measurement strategies: Hadamard (green) and basis rotation (red with hatching). The vertical dashed line shows the ideal statevector simulation result. The bin width is automatically determined by the Freedman-Diaconis rule.