Simulating light atomic nuclei in a quantum computer

Abstract

Solving the dynamics of many-body systems is one of the most challenging problems in modern science. For this application, classical computational techniques face significant limitations, mainly the need to handle large Hilbert spaces. Quantum computation, particularly through hybrid quantum and classical algorithms, has started gaining popularity, offering a promising new approach. This work characterizes the Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) algorithm by simulating 6Be, 12C and 14N nuclei via the shell model on an ideal quantum computer. It focuses on the ADAPT-VQE’s response to the inherent statistical noise that results from the finite number of measurements (“shots”) performed. In particular, the study quantifies the energy convergence with measurement shots, while demonstrating how statistical noise impacts variational parameter optimization. The results show that this impact leads to a final energy error that scales with Nshots following a power law distinct from the standard statistical limit and particular for each nucleus. Furthermore, the mean energy converges towards the ideal value as the optimizer performs more effectively as Nshots increases