Simulation of an Exactly-Solvable Nuclear Model on NISQ Devices and Simulators

Noisy Intermediate-Scale Quantum (NISQ) computers are promising tools but are not yet able to perform fault tolerant quantum simulations We use simulation of the exactly solvable Lipkin-Meshkov-Glick (LMG) model as a benchmarking tool for several NISQ devices, simulators and methods. We also discuss qualities of non-compact bosonic encodings that are not present in fermionic encodings such as the Jordan-Wigner, Parity or Bravyi-Kitaev. Simulation of the N-particle LMG Hamiltonian with the Variational Quantum Eigensolver (VQE) requires O(N) qubits and O(N) gates. Estimation of the LMG Hamiltonian expectation value requires O(1) distinct measurement bases for any number of particles. The classical resources required to prepare and solve the problem scale polynomially with N. Because both the classical and quantum resources required scale efficiently as a function of N, simulation of the LMG model is useful as a benchmarking tool even at large problem sizes.