Nuclear Many-Body Systems as Benchmarks for Quantum Computing

Abstract

We present a framework for benchmarking quantum algorithms for nuclear many-body systems based on realistic nuclear Hamiltonians such as chiral effective field theory. To this end, we introduce a workflow that maps nuclear interactions in second quantization formalism to qubit Hamiltonians. This enables the systematic construction of benchmark instances spanning no-core and valence-space formulations with two-body (NN) and selected three-body (3N) interactions. Then, we proceed to provide resource estimates for three representative eigenvalue algorithms: Quantum Phase Estimation, Quantum Krylov methods, and Observable Dynamic Mode Decomposition. We compare their resource requirements in terms of T-gate counts and system size, and examine the impact of model-space choices and many-body interactions. The primitives included in our analysis are Trotterization, Qubitization, and Quantum Singular Value Transformation. Our results quantify scaling trends across algorithms and problem classes, and provide a basis for consistent comparisons of quantum approaches to nuclear many-body problems. The implementation is provided by the NuQuLib software stack.