Quantum computing can potentially provide advantages for specific computational tasks. The simulation of fermionic systems is one such task that lends itself well to quantum computation, with applications in nuclear physics and electronic systems. Here we present work in which we use a variance minimization method to find the full spectrum of energy eigenvalues of the Lipkin-Meshkov-Glick model, an exactly solvable nuclear shell model type system. We perform these calculations using both quantum simulators and real quantum hardware accessed via IBM cloud-based quantum computers. Using these IBM quantum computers we are able to obtain all eigenvalues for the cases of three and seven fermions (nucleons) in the Lipkin-Meshkov-Glick model. We further show a simulated result for a realistic calculation of ${}^6\mathrm{Li}$ with a shell model interaction which performs equivalently to the Lipkin-Meshkov-Glick model.

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• Energy levels
• Models based on symmetries
• Nuclear many-body theory
• Quantum circuits
• Quantum computation
• Quantum simulation
• Shell model