Studying the response of quantum systems is essential for gaining deeper insights into the fundamental nature of matter and its behavior in diverse physical contexts. Computation of nuclear response is critical for many applications, but its spectroscopically accurate description in medium-heavy nuclei in wide energy ranges remains particularly challenging because of the complex nature of nuclear quantum states in the high-level-density regime. Herein, we push the limits of configuration complexity in the classical computation of the nuclear response and present an algorithm with a quantum benefit for treating complex configurations. The classical computational method of approaching spectroscopic accuracy is implemented for medium-heavy nuclei and pioneered for the dipole response of 120Sn, while the quantum algorithm reaching the exact solution is realized for the Lipkin Hamiltonian to unravel the emergence of collectivity at strong coupling.
Studying the response of quantum systems is essential for gaining deeper insights into the fundamental nature of matter and its behavior in diverse physical contexts. Computation of nuclear response is critical for many applications, but its spectroscopically accurate description in medium-heavy nuclei in wide energy ranges remains particularly challenging because of the complex nature of nuclear quantum states in the high-level-density regime. Herein, we push the limits of configuration complexity in the classical computation of the nuclear response and present an algorithm with a quantum benefit for treating complex configurations. The classical computational method of approaching spectroscopic accuracy is implemented for medium-heavy nuclei and pioneered for the dipole response of 120Sn, while the quantum algorithm reaching the exact solution is realized for the Lipkin Hamiltonian to unravel the emergence of collectivity at strong coupling.
Abstract Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions 1–3 to quantum chemistry 4–6 and from atomic and molecular systems 7–9 to nuclear physics 10–14 . One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations 15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions 17,18 and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations 19,20 .
Atomic nuclei are important laboratories for exploring and testing new insights into the universe, such as experiments to directly detect dark matter or explore properties of neutrinos. The targets of interest are often heavy, complex nuclei that challenge our ability to reliably model them (as well as quantify the uncertainty of those models) with classical computers. Hence there is great interest in applying quantum computation to nuclear structure for these applications. As an early step in this direction, especially with regards to the uncertainties in the relevant quantum calculations, we develop circuits to implement variational quantum eigensolver (VQE) algorithms for the Lipkin-Meshkov-Glick model, which is often used in the nuclear physics community as a testbed for many-body methods. We present quantum circuits for VQE for two and three particles and discuss the construction of circuits for more particles. Implementing the VQE for a two-particle system on the IBM Quantum Experience, we identify initialization and two-qubit gates as the largest sources of error. We find that error mitigation procedures reduce the errors in the results significantly, but additional quantum hardware improvements are needed for quantum calculations to be sufficiently accurate to be competitive with the best current classical methods.
We investigate the quantum equation of motion (qEOM), a hybrid quantum-classical algorithm for computing excitation properties of a fermionic many-body system, with a particular emphasis on the strong-coupling regime. The method is designed as a stepping stone towards building more accurate solutions for strongly coupled fermionic systems, such as medium-heavy nuclei, using quantum algorithms to surpass the current barrier in classical computation. Approximations of increasing accuracy to the exact solution of the Lipkin-Meshkov-Glick Hamiltonian with N=8 particles are studied on digital simulators and IBM quantum devices. Improved accuracy is achieved by applying operators of growing complexity to generate excitations above the correlated ground state, which is determined by the variational quantum eigensolver. We demonstrate explicitly that the qEOM exhibits a quantum benefit due to the independence of the number of required quantum measurements from the configuration complexity. Postprocessing examination shows that quantum device errors are amplified by increasing configuration complexity and coupling strength. A detailed error analysis is presented, and error mitigation based on zero noise extrapolation is implemented.
Quantum computing is increasingly offering concrete solutions toward the simulation of nuclear structure, with the potential to overcome the exponential scaling that limits classical diagonalization methods in large spaces. A particularly efficient encoding scheme, based on collective like-nucleon pairing modes, reduces the qubit requirements by half and avoids the non-local operator strings of standard fermion-to-qubit mappings. While this quasiparticle framework provides accurate results for semimagic nuclei, it does not adequately describe open-shell systems where proton-neutron correlations become important. In this work, we apply Brillouin-Wigner perturbation theory to systematically improve the quasiparticle description of open-shell nuclei in the sd shell, reaching an energy relative error below 0.2% compared to the nuclear shell model. Furthermore, to make the effective Hamiltonian suitable for quantum simulation, we introduce a mean-field Hartree-Fock approximation of the non-quasiparticle resolvent, achieving ground-state energies typically within 2% of the exact shell-model result. This represents a systematic improvement over the bare quasiparticle Hamiltonian while remaining within the reach of near-term quantum devices.
Nonperturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with nonperturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons ($2\mathrm{q}\ensuremath{\bigotimes}2\mathrm{phonon}$), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of 42,48Ca and 68Ni nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.
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.