Variational quantum eigensolver ansatz for the J1−J2 -model

Abstract

The ground state properties of the two-dimensional ${J}_{1}\ensuremath{-}{J}_{2}$-model are very challenging to analyze via classical numerical methods due to the high level of frustration. This makes the model a promising candidate for which quantum computers could be helpful to possibly explore regimes that classical computers cannot reach. The ${J}_{1}\ensuremath{-}{J}_{2}$-model is a quantum spin model composed of Heisenberg interactions along the rectangular lattice edges and along diagonal edges between next-nearest-neighbor spins. We propose an ansatz for the variational quantum eigensolver to approximate the ground state of an antiferromagnetic ${J}_{1}\ensuremath{-}{J}_{2}$ Hamiltonian for different lattice sizes and different ratios of ${J}_{1}$ and ${J}_{2}$. Moreover, we demonstrate that this ansatz can work without the need for gates along the diagonal next-nearest-neighbor interactions. This simplification is of great importance for solid-state-based hardware with qubits on a rectangular grid, where it eliminates the need for swap gates. In addition, we provide an extrapolation for the number of gates and parameters needed for larger lattice sizes, showing that these are expected to grow linearly in the qubit number up to lattice sizes which eventually can no longer be treated with classical computers.