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.
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.
Abstract The nuclear binding energy problem is one of the fundamental challenges of the nuclear many-body problem, as calculating the corresponding binding energies by various approximate methods remains computationally challenging for a wide range of nuclei. In this work, a binding energy model derived from quantum computational approaches to nuclear physics is proposed and implemented in a quantum computer simulator to address the nuclear binding energy problem. The goal is to develop a framework capable of calculating the binding energies of multiple nuclei within a unified scheme. To this end, appropriate potential expressions are selected and tuned to accommodate varying nuclear properties. The defined Hamiltonian is parameterized and transformed into a form suitable for implementation on a quantum computer. Depending on the number of nucleons, the program is run on 2 to 12 qubits to obtain the minimum eigenvalue of the Hamiltonian corresponding to the ground state energy (binding energy of the nucleus) according to the variational principle of quantum mechanics. This framework provides, the binding energies of the first 29 nuclei with a total deviation of 16.86% ( 2 H, 3 H, 3 He, 4 He, 6 He, 8 He, 6 Li, 7 Li, 8 Li, 9 Li, 11 Li, 7 Be, 8 Be, 9 Be, 10 Be, 11 Be, 12 Be, 8 B, 9 B, 10 B, 11 B, 12 B, 9 C, 10 C, 11 C, 12 C, 11 N, 12 N, 12 O) obtained by quantum computation following the steps of Variational Quantum Eigensolver (VQE). These results support the feasibility of the proposed approach for nuclear binding energy calculations. In this sense, this work contributes to quantum computing and nuclear physics by providing a model able to calculate the binding energies for the first 29 nuclei using quantum computer simulator and offers a promising route for future large-scale applications.
We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.
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.
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 6−9 Li from the p -shell, 18 F from the sd -shell, and two heavier nuclei ( 210 Po, and 210 Pb). We run circuits representing their ground states on a noisy simulator (IBM’s FakeFez backend) and quantum hardware ( ibm_pittsburgh ). For heavier nuclei, we demonstrate the feasibility of simulating 210 Po and 210 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.
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.
Much has been talked about quantum computers. Today they are working on difficult simulations, so we can already congratulate the college of researchers at the Oak Ridge National Laboratory as the world's first to successfully simulate an atomic nucleus using a quantum computer. The results that were published in the physical examination letters demonstrate the huge capacity of quantum systems to calculate the problems of nuclear physics and to be able to be successfully used in the future for special and complex simulations. It is already known that quantum calculus, which is based on the quantum principles of matter and which was proposed by American physicist Richard Feynman in the early 1980s, unlike the ordinary bits of normal computers today, uses the qubit units used by quantum computers to store information in two-state systems, such as electrons or photons, considered simultaneously in all possible quantum states (essentially a phenomenon known as overlapping). In October 2017, a multidisciplinary ORNL team began working on codes to perform various simulations on quantum computers such as IBM QX5 and Righetti 19Q within a DOE Quantum Testbed Pathfinder project in an effort to verify and validate various scientific applications on different types of quantum hardware. Today, quantum computers have potential applications in cryptography, artificial intelligence and weather forecasting, as each additional qubit clings in some way inextricably from the others, thus exponentially increasing the number of possible results for the final measured state. Obviously, this huge benefit also has negative effects on the system, because errors can in turn exponentially increase the size of the problem and the final results even. However, it is hoped that in the future on the basis of much-improved hardware, researchers will be able to solve problems that cannot be solved today using current calculation methods. In the present paper the authors propose an original method of rapid theoretical determination with great precision of the dimensions of all elementary particles, the method which, although predicting results similar to those obtained by other theoreticians, still has the advantage of its simplicity, of its general applicability, that is of its universality and especially this new method is a precious tool in the work of scientists worldwide to understand matter at its elementary level. Even though we would have expected that the size of a deuteron would be larger (double) than that of one component particle (of a proton or neutron), at the same velocity, the theory (20-21) demonstrates the opposite. By fusing two free nucleons, a proton and a neutron, a deuterium nucleus is obtained with smaller dimensions than its two components, which makes the energy of rejection between two Deuteron cores much larger than we would have waited. That's why the fusion reaction between two Deuterons is even more difficult than was suspected, even when they are accelerating.