Quantum simulation of nuclear shell model: bridging theory and hardware limitations

In this work, we introduce a new qubit mapping strategy for the Variational Quantum Eigensolver (VQE) applied to nuclear shell model calculations, where each Slater determinant (SD) is mapped to a qubit, rather than assigning qubits to individual single-particle states. While this approach may increase the total number of qubits required in some cases, it enables the construction of simpler quantum circuits that are more compatible with current noisy intermediate-scale quantum (NISQ) devices. We apply this method to seven nuclei, including four lithium isotopes ⁽⁶⁻⁹⁾Li from p-shell, ¹⁸F from sd-shell, and two heavier nuclei (²¹⁰Po, and ²¹⁰Pb). We run those circuits representing their g. s. on noisy simulator (FakeFez backend) and quantum hardware (ibmₚittsburgh). For heavier nuclei, we demonstrate the feasibility of simulating ²¹⁰Po and ²¹⁰Pb as 22- and 29-qubit systems, respectively. Additionally, we employ Zero-Noise Extrapolation (ZNE) via two-qubit gate folding to mitigate errors in both simulated and hardware-executed results. Post-mitigation, the best results show less than 4 % deviation from shell model predictions across all nuclei studied. This SD-based qubit mapping proves particularly effective for lighter nuclei and two-nucleon systems, offering a promising route for near-term quantum simulations in nuclear physics.