Scalable nuclear shell model calculations on noisy quantum computers

How can current Noisy Intermediate-Scale Quantum (NISQ) hardware be utilized to perform large-scale nuclear shell model calculations that normally face severe memory bottlenecks and scaling limits on classical supercomputers?

The authors implement a hybrid quantum-classical Sample-based Quantum Diagonalization (SQD) framework for nuclear shell models. Using a shallow quantum ansatz derived from Unitary Coupled Cluster Singles and Doubles (UCCSD) operators, real quantum hardware acts purely as a configuration sampler. The resulting probabilistic measurement bitstrings are processed classically to discard noise and non-physical states, construct a reduced active subspace, and perform exact matrix diagonalization. The method is first benchmarked on 38Ar and then scaled to study the neutron-rich 32Mg nucleus within an sdpf-m model space, comparing execution times and memory scaling against standard variational quantum algorithms (like VQE) and classical solvers (dense, sparse, and Lanczos).

SQD successfully reproduces classical exact diagonalization benchmarks for 38Ar in just 3.16 seconds, significantly outperforming VQE in execution speed. When scaled to 32Mg, SQD bypasses the 768 GB RAM limitations of the classical high-performance computing system. For 40 spin-orbitals, SQD achieves ground-state energy estimates closer to experimental values than resource-starved classical calculations, and it maintains feasibility where classical solvers and VQE encounter out-of-memory or deep-circuit noise errors.

Exact nuclear shell-model calculations scale exponentially with the number of orbitals, quickly exhausting classical supercomputing memory. While variational quantum algorithms like VQE suffer from deep-circuit noise and expensive feedback loops on noisy hardware, SQD decouples state optimization from the QPU. This provides a pragmatic, noise-resilient pathway toward practical quantum advantage for complex many-body quantum systems.