Assessment of the variational quantum eigensolver: application to the Heisenberg model

• URL: http://arxiv.org/abs/2201.05065v2
• Date: Fri, 17 Jun 2022 07:16:32 GMT
• Title: Assessment of the variational quantum eigensolver: application to the Heisenberg model
• Authors: Manpreet Singh Jattana, Fengping Jin, Hans De Raedt, Kristel Michielsen
• Abstract summary: We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present and analyze large-scale simulation results of a hybrid quantum-classical variational method to calculate the ground state energy of the anti-ferromagnetic Heisenberg model. Using a massively parallel universal quantum computer simulator, we observe that a low-depth-circuit ansatz advantageously exploits the efficiently preparable N\'{e}el initial state, avoids potential barren plateaus, and works for both one- and two-dimensional lattices. The analysis reflects the decisive ingredients required for a simulation by comparing different ans\"{a}tze, initial parameters, and gradient-based versus gradient-free optimizers. Extrapolation to the thermodynamic limit accurately yields the analytical value for the ground state energy, given by the Bethe ansatz. We predict that a fully functional quantum computer with 100 qubits can calculate the ground state energy with a relatively small error.

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