Toward $\textit{Ab Initio}$ Quantum Simulations of Atomic Nuclei Using Noisy Qubits

Abstract

Quantum computers are expected to provide a ultimate solver for quantum many-body systems, although it is a tremendous challenge to achieve that goal on current noisy quantum devices. This work illustrated quantum simulations of ab initio no-core shell model calculations of $^3$H with chiral two-nucleon and three-nucleon forces. The measurement costs are remarkably reduced by using the general commutativity measurement together with the asymptotic optimization. In addition, the noise causes serious contaminations of configurations with undesired particle numbers, and the accuracies are much improved by applying the particle number projected measurement. By tackling the efficiency and noise issues, this work demonstrated a substantial step toward ab initio quantum computing of atomic nuclei.

Figures (2)

• Figure 1: The scalability of measurement costs with increasing model spaces. (a) Comparison of measurement groups for Hamiltonian with $NN$ forces by different schemes: the naive case without grouping, QWC grouping, GC grouping, MBPT2-related terms with and without GC grouping. (b) Comparison of parameters obtained by optimizing terms up to MBPT2 and MBPT3 levels, respectively. (c) Measurement groups for Hamiltonian with $NN$ and 3$N$ forces as the model space increases.
• Figure 2: Results with JW and BK mappings as the noise scale $a$ varies. (a) The magnitude of components with undesired particle numbers due to noise contamination with increasing $a$. (b) The entanglement entropy of each qubit without noise and with $a$=0.5 are shown. The entanglement entropy obtained with symmetry projection is also shown. (c) The total binding energies (in MeV) of $^3$H with only $NN$ forces. The open-symbols indicate the original measured energies. The solid-symbols indicate the energies with symmetry projection in measurements of diagonal terms, while other contributions are unchanged. The exact values from NCSM calculations are shown by the dashed line. (d) The measured total energies (in MeV) with $NN$ plus 3$N$ forces, in which diagonal terms are measured with symmetry projection.