Shadow-based quantum subspace algorithm for the nuclear shell model

TL;DR

This paper introduces a novel quantum algorithm combining classical shadow and subspace diagonalization to efficiently estimate nuclear ground state energies on NISQ devices, demonstrating improved accuracy with more measurements.

Contribution

The paper presents a new shadow-based quantum subspace algorithm tailored for nuclear shell models, advancing quantum ground state energy calculations in the NISQ era.

Findings

Accuracy improves with increased shots following Heisenberg scaling

Effective for Cohen-Kurath and USD shell models

Demonstrates potential for quantum advantage in nuclear physics

Abstract

In recent years, researchers have been exploring the applications of noisy intermediate-scale quantum (NISQ) computation in various fields. One important area in which quantum computation can outperform classical computers is the ground state problem of a many-body system, e.g., the nucleus. However, using a quantum computer in the NISQ era to solve a meaningful-scale system remains a challenge. To calculate the ground energy of nuclear systems, we propose a new algorithm that combines classical shadow and subspace diagonalization techniques. Our subspace is composed of matrices, with the basis of the subspace being the classical shadow of the quantum state. We test our algorithm on nuclei described by Cohen-Kurath shell model and USD shell model. We find that the accuracy of the results improves as the number of shots increases, following the Heisenberg scaling.