Quantum computational simulation to calculate the deuteron binding energy

Omar Shehab, K. A. Landsman, Yunseong Nam +5 more

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansatze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion, and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of ${E}_{4}=\ensuremath{-}2.220\ifmmode\pm\else\textpm\fi{}0.179$ MeV may be compared with the exact deuteron ground-state energy $\ensuremath{-}2.224$ MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.

Richard L. Liboff

ChangYue Zhu, Gang 刚 Li 李, Mao Song +1 more

Isaac Hobday, P. D. Stevenson, James Benstead

Calculations of nuclear properties and nuclear models are performed using quantum computing algorithms on simulated and real quantum computers. The models are a realistic calculation of deuteron binding based on effective field theory, and a simplified two-level version of the nuclear shell model. A method of reducing the number of qubits needed for practical calculation is presented, the reduction being with respect to that used when the standard Jordan-Wigner encoding is used. Its efficacy is shown in the case of the deuteron binding and shell model. A version of the variational quantum eigensolver in which all eigenstates in a spectrum are targeted on an equal basis is shown. The method involves finding the minima of the variance of the Hamiltonian, and its ability to find the full spectrum of small version of the simplified shell model is presented.

PENG Baining1,  CUI Ying1,  YAN Yuliang1,  GAO Zaochun1,  WEI Shijie2 ,  ZHANG Yingxun1, 3, 4

Accurate calculations of nuclear binding energies in theory is a long-standing problem in nuclear physics, as it provides critical insights the effective interactions and structures of atomic nuclei. Currently, there are severe limitations in theory due to the exponential growth of the Hilbert space with increasing nucleon number, i.e., curse of the dimension. There are some effort to mitigate this problem by using the state-of-art methods, such as the machine learning and quantum computing. Recent advances in quantum computing have opened new avenues for addressing these challenges, enabling the direct simulation of nuclear many-body systems on quantum hardware. In this work, a detailed study on the calculation of nuclear binding energies using the full quantum eigensolver (FQE) algorithm, implemented on a real quantum processor, i.e. Quafu, was presented. Two nuclear systems (2H and 6He) were investigated. The deuteron, as the simplest bound nucleus with just one proton and one neutron, serves as an ideal benchmark for testing quantum algorithms, FQE. 6He, a light, two-valence neutron nucleus, was used for estimating the ability of the Quafu quantum cloud platform and its “Baihua” quantum chip. Our results demonstrate that for the deuteron, the FQE algorithm on the “Baihua” quantum processor achieves a higher level of accuracy compared to previously reported results obtained using the variational quantum eigensolver (VQE) on the IBM_QX5 and IBM_19Q platforms, as discussed in Dumitrescu’s article. For 6He, the FQE-calculated binding energy shows accuracy comparable to recent VQE-based calculations reported in Yoshida’s article. These findings highlight the feasibility of performing precise nuclear structure calculations on near-term quantum devices and underscore the potential of the FQE approach for future applications in nuclear physics. Overall, this study extends the scope of quantum computing in nuclear physics by demonstrating that the FQE algorithm can serve as a practical and accurate tool for computing binding energies on real quantum hardware. The results provide a benchmark for future developments in quantum simulations of nuclei and suggest promising directions for scaling these methods to larger nuclear systems, ultimately contributing to a deeper understanding of nuclear structure and dynamics.

Matthias Troyer