Abstract We have obtained the energy of the deuteron on a quantum simulator using the variational quantum eigensolver. We have employed realistic two-body interactions, namely, chiral N4LO and AV 18 , thus incorporating the role of tensor forces. These interactions are subsequently evolved to low resolution scales using the similarity renormalization group approach with parameter λ . The deuteron ground state energy has been calculated in the truncated harmonic oscillator basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of harmonic oscillator basis states (hence qubits) needed for computing the energy to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing λ . We have analysed the extent of entanglement between oscillator modes using concurrence as the entanglement quantifier. It is seen that the entanglement decreases as λ is lowered from the bare value to ∼1.0 fm −1 independent of the form of the bare interaction and the number of harmonic oscillator basis states.
Abstract We have obtained the energy of the deuteron on a quantum simulator using the variational quantum eigensolver. We have employed realistic two-body interactions, namely, chiral N4LO and AV 18 , thus incorporating the role of tensor forces. These interactions are subsequently evolved to low resolution scales using the similarity renormalization group approach with parameter λ . The deuteron ground state energy has been calculated in the truncated harmonic oscillator basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of harmonic oscillator basis states (hence qubits) needed for computing the energy to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing λ . We have analysed the extent of entanglement between oscillator modes using concurrence as the entanglement quantifier. It is seen that the entanglement decreases as λ is lowered from the bare value to ∼1.0 fm −1 independent of the form of the bare interaction and the number of harmonic oscillator basis states.
We present the quantum simulation of the deuteron to calculate its binding energy using the variational quantum eigensolver, which is based on a hybrid quantum-classical approach. Apart from a commonly used Hamiltonian derived from pionless effective field theory, we consider the interaction which can be easily studied with conventional classical methods but the corresponding operator leading to nonzero off-tridiagonal matrix elements. To map the many-body basis states on the qubit states, three encodings are explored, namely, one-hot, Bravyi-Kitaev, and the Gray code. We perform a generalized transformation for many-body operators in Gray code encoding, and simulate the Hamiltonians with nonzero off-tridiagonal matrix elements. Furthermore, the analyses of the relative efficiency of all encodings and corresponding transformations are carried out using the noise model of a real IBM quantum device. We demonstrate that the Gray code is more efficient for a large basis, irrespective of the form of potential and the presence of hardware noise.
Background: Quantum simulations offer the potential to predict the structure and dynamics of nuclear many-body systems that are beyond the capabilities of classical computing. Generally, preparing the ground state of strongly interacting many-body systems relevant to nuclear physics is, however, inefficient, even using ideal quantum computers. In addition, currently available noisy intermediate-scale quantum (NISQ) era quantum devices possess modest numbers of qubits, limiting the size of quantum many-body systems that can be simulated. In this context, a reformulation of the quantum many-body problems using truncated model spaces and Hamiltonians is desirable to make them more amenable to near-term quantum computers. The importance of symmetries in low-energy theories, including effective field theories (EFTs), lattice quantum chromodynamics (QCD), and effective model spaces for nuclear systems, in particular their interplay with the reduction of active Hilbert spaces, is well known. Lesser known is the fact that the noncommutivity of some symmetries and truncations of the model space can be profitably combined with variational calculations to rearrange the entanglement into localized structures and enable more efficient simulations.Purpose: The goal of the present study is to explore and utilize the noncommutivity of symmetries and model-space truncations of quantum many-body systems important to nuclear physics, particularly in combination with variational algorithms for quantum simulations and effective Hamiltonian learning.Method: We introduce an iterative hybrid classical-quantum algorithm, the Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian, thereby rearranging entanglement into the effective model space, and the associated ground-state wave function. Quantum simulations, using classical computers and IBM's superconducting-qubit quantum computers, are performed to demonstrate the HL-VQE algorithm, in the context of the Lipkin-Meshkov-Glick (LMG) model of interacting fermions, where the Hamiltonian transformation corresponds to an orbital rotation. We use a mapping where the number of qubits scales with the logarithm of the size of the effective model space, rather than the particle number.Results: HL-VQE is found to provide an exponential improvement in LMG-model calculations of the ground-state energy and wave function, compared to naive truncations without Hamiltonian learning, throughout a significant fraction of the Hilbert space. In the context of EFT, this corresponds to counterterms scaling exponentially with the cutoff as opposed to power law. Implementations on IBM's QExperience quantum computers and simulators for one- and two-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions.Conclusions: For a range of parameters defining the LMG model, the HL-VQE algorithm is found to have better scaling of quantum resources requirements than previously explored algorithms. In particular, the HL-VQE scales efficiently over a large fraction of the model space, in contrast to VQE alone. This work constitutes a step in the development of entanglement-driven quantum algorithms for descriptions of nuclear many-body systems. This, in part, leverages the potential of noisy intermediate-scale quantum (NISQ) devices. The exponential scaling of counterterms observed in this study suggests the possibility of more general applicability to other nonperturbative EFTs.
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.
Anharmonic potential quantum system play crucial role in physics as they provide a more realistic description of oscillatory phenomena, which often deviate from the idealized harmonic model. However, simulating such system on classical computers is highly challenging due to nonlinear interactions, large state spaces, and the exponential scaling of memory and computational resources. In this work, quantum simulation is employed to model a quantum anharmonic oscillator (QAHO) using a 3-qubit system implemented on IBM's Quantum Experiences platform. A quantum circuit with a filter-based design and Toffoli gates is constructed to track quantum state evolution, capturing key phenomena like quantum revival. The framework is further extended to n-qubit system to enhance resolution and scalability. For energy estimation, the Variational Quantum Eigensolver (VQE) with a TwoLocal ansatz and variational Quantum Deflation (VQD), are used to compute ground and excited state energies. The proposed approach achieves high accuracy with an error of only 1.11% compared to exact methods. Notably, VQE outperforms classical approximations such as perturbation theory (error 6.71%) and the Wentzel-Kramers-Brillouin (WKB) approximation(error 5.36%), yielding more precise energy values. These results highlight the potential of quantum simulation and VQD as effective tools for investigating complex quantum system, paving the way for future application in quantum chemistry and materials science as quantum hardware continues to advance.
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.
molecule, emphasizing practical implementation and performance on current quantum hardware. Our research presents a comparative study of HEA and UCCSD ansätze on noiseless and noisy simulations and implements VQE on recent IBM quantum computer noise models and a real quantum computer, IBM Fez, providing a fully functional code employing Qiskit 1.2. Our experiments confirm UCCSD's reliability in ideal conditions, while the HEA demonstrates greater robustness to hardware noise, achieving chemical accuracy on state-vector simulation (SVS). The results reveal that achieving ground-state energy within chemical accuracy is feasible without error mitigation during VQE convergence. We demonstrate that current quantum devices effectively optimize circuit parameters despite misestimating simulated energies. The SVS-evaluated energies provide a more accurate representation of the solution quality compared to QPU-estimated energy values, indicating that VQE converges to the correct ground state despite quantum noise. Our study also applies noise mitigation as a postprocessing technique, using zero-noise extrapolation (ZNE) on a real quantum computer. The detailed methodologies presented in this study, including Hamiltonian construction and Fermionic-to-qubit transformations, facilitate flexible adaptation of the VQE approach for various algorithm variants and across different levels of algorithmic implementation.