Quantum-Enhanced Computing for the Antiferromagnetic J 1 − J 2 $J_1-J_2$ Heisenberg Model

Abstract

The variational quantum eigensolver (VQE) has recently been demonstrated for solving the challenging Heisenberg Antiferromagnet (HAFM) models. Apart from the ground state energy, many important issues such as excited states and general frustration for HAFM are worth investigating, which have only been partially solved by classical methods and rarely by quantum approaches. Here, VQE is applied to the GPU quantum simulator to calculate the excited states of a $J_1$-$J_2$ HAFM model on both square and kagome lattices. The invariant subspace property is analyzed during the process of VQE and hence the even-fold degeneracy is explained that is difficult to interpret using classical methods. Moreover, the VQE results for different $J_2$/$J_1$ ratios show a more efficient way to observe the phase transition in this model. The advantageous properties of VQE are demonstrated for exploring fundamental physical mechanisms.