Quasiparticle pairing encoding of atomic nuclei for quantum annealing

TL;DR

The paper tackles the high fermionic-operator encoding cost in nuclear shell-model simulations on quantum devices by introducing a quasiparticle pairing encoding that maps paired nucleon modes to hardcore bosons. It constructs a projected quasiparticle Hamiltonian $H_Q=\mathbb{Q}H\mathbb{Q}$ and demonstrates that, for semimagic nuclei in the $sd$ and $pf$ shells and tin isotopes, $H_Q$ achieves high ground-state accuracy with small energy errors and high fidelities. The authors then benchmark the approach against full configuration interaction and show that quantum-annealing simulations using $H_Q$ require 2–3 orders of magnitude fewer CNOT gates than standard Jordan–Wigner implementations, highlighting a major resource reduction. The results indicate a practical route to scalable quantum simulations of nuclear structure on digital and hybrid platforms, while also outlining limitations for open-shell nuclei and proposing future extensions via hybrid representations or perturbative corrections.

Abstract

Quantum computing is emerging as a promising tool in nuclear physics. However, the cost of encoding fermionic operators hampers the application of algorithms in current noisy quantum devices. In this work, we analyze an encoding scheme based on pairing nucleon modes. This approach significantly reduces the complexity of the encoding, while maintaining a high accuracy for the ground states of semimagic nuclei across the $sd$ and $pf$ shells and for tin isotopes. In addition, we also explore the encoding ability to describe open-shell nuclei within the above configuration spaces. When this scheme is applied to a trotterized quantum adiabatic evolution, our results demonstrate a computational advantage of up to three orders of magnitude in CNOT gate count compared to the standard Jordan-Wigner encoding. Our approach paves the way for efficient quantum simulations of nuclear structure using quantum annealing, with applications to both digital and hybrid quantum computing platforms.

Figures (3)

• Figure 1: Energy relative error $\Delta_Q E$ (left panel) and infidelity $1-F_Q$ (right panel) of the ground state obtained with $H_Q$ with respect to the exact FCI result, for nuclei across the $sd$ shell in terms of their number of protons ($Z_p$) and neutrons ($N_n$) in the valence space. Darker colors indicate more accurate results obtained with $H_Q$.
• Figure 2: Energy relative error $\Delta_Q E$ (blue bars, left scale) and infidelity $1-F_Q$ (red bars, right scale) compared to FCI results, for Ca isotopes and $^{44}$Ti in the $pf$ shell, and Sn isotopes. The $^{42}$Ca and $^{102}$Sn results are below the scale.
• Figure 3: Number of CNOT gates required in the trotterized quantum-annealing circuits for $H_\text{NSM}$ (black stars) and $H_Q$ (violet circles), needed to reach the same fidelity for the ground state of each nucleus (see text for details).