A low-circuit-depth quantum computing approach to the nuclear shell model

Abstract

In this work, we introduce a new qubit mapping strategy for the Variational Quantum Eigensolver (VQE) applied to nuclear shell model calculations, where each Slater Determinant (SD) is mapped to a qubit, rather than assigning qubits to individual single-particle states. While this approach may increase the total number of qubits required in some cases, it enables the construction of simpler quantum circuits that are more compatible with current noisy intermediate-scale quantum (NISQ) devices. We apply this method to seven nuclei: Four lithium isotopes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{6-9}$$\end{document}Li from the p-shell, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{18}$$\end{document}F from the sd-shell, and two heavier nuclei (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{210}$$\end{document}Po, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{210}$$\end{document}Pb). We run circuits representing their ground states on a noisy simulator (IBM’s FakeFez backend) and quantum hardware (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ibm\_pittsburgh$$\end{document}). For heavier nuclei, we demonstrate the feasibility of simulating \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{210}$$\end{document}Po and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^{210}$$\end{document}Pb as 22- and 29-qubit systems, respectively. Additionally, we employ Zero-Noise Extrapolation (ZNE) via two-qubit gate folding to mitigate errors in both simulated and hardware-executed results. Post-mitigation, the best results show less than 4 % deviation from shell model binding energy predictions across all nuclei studied. This SD-based qubit mapping proves particularly effective for lighter nuclei and two-nucleon systems, offering a promising route for near-term quantum simulations in nuclear physics.