Quantum Simulation of Nuclear Shell Model Using GCM-Based Methods on NISQ Devices

How can we effectively simulate the low-lying energy spectra of strongly correlated nuclear systems on current Noisy Intermediate-Scale Quantum (NISQ) hardware? The authors seek to overcome the limitations of traditional variational quantum algorithms—such as complex energy landscapes and high optimization costs—by adapting the classical Generator Coordinate Method (GCM) for quantum devices.

The authors implement a hybrid quantum-classical framework called Quantum GCM (QuGCM). They construct a basis of non-orthogonal quantum states by applying symmetry-adapted Unitary Coupled-Cluster (UCC) operators to Hartree-Fock reference states. Instead of performing full variational optimization, they solve a generalized eigenvalue problem (the Hill-Wheeler equation) on a classical computer using overlap and Hamiltonian kernels computed on the quantum device. To further optimize, they introduce the Adaptive Generator Coordinate Inspired method (ADAPT-GCIM), which iteratively selects only the most significant generator excitations based on energy gradients, minimizing the required circuit depth.

The study demonstrates that both QuGCM and ADAPT-GCIM successfully reproduce energy spectra for the deuteron, 6Li, and 38Ar that align with classical diagonalization results. The authors show that these methods are robust against noise and hardware constraints. Furthermore, they compare fermionic encoding strategies and find that Gray code (GC) mapping significantly outperforms the standard Jordan-Wigner (JW) transformation of one-hot encoding by reducing circuit complexity and enhancing state preparation fidelity.

This work provides a scalable, NISQ-friendly path for nuclear physics simulations. By shifting the burden from complex parameter optimization (as seen in VQE) to a subspace diagonalization approach, the framework is less susceptible to the barren plateaus and noise-induced errors that typically plague near-term quantum simulations of strongly correlated systems.