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

TL;DR

This paper evaluates the variational quantum eigensolver's effectiveness in calculating the ground state energy of the Heisenberg model, demonstrating promising results with large-scale simulations and potential for future quantum computers.

Contribution

It provides a comprehensive analysis of ansatz choices, initial states, and optimization methods, highlighting the method's scalability and accuracy in simulating quantum many-body systems.

Findings

Low-depth circuits effectively exploit the Néel state.

Extrapolation matches the Bethe ansatz for thermodynamic limit.

A 100-qubit quantum computer can achieve small error in energy calculation.

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.