Obtaining Ground States of the XXZ Model Using the Quantum Annealing with Inductively Coupled Superconducting Flux Qubits

Obtaining ground states of Hamiltonians is important in the condensed matter physics and the quantum chemistry. The interaction Hamiltonians typically contain not only diagonal but also off-diagonal elements. Although quantum annealing provides a way to obtain a ground state of a Hamiltonian, we can only use the Hamiltonian with Ising interaction by using currently available commercial quantum annealing devices. In this work, we propose a quantum annealing for the XXZ model, which contains both Ising interaction and energy-exchange interaction, by using inductively coupled superconducting flux qubits. The key idea is to use a recently proposed spin-lock quantum annealing where the qubits are driven by microwave fields. As long as the rotating wave approximation is valid, the inductive coupling between the superconducting flux qubits produces the desired Hamiltonian in the rotating frame, and we can use such an interaction for the quantum annealing while the microwave fields driving play a role of the transverse fields. To quantify the performance of our scheme, we implement numerical simulations, and show that we can obtain ground states of the two-dimensional Heisenberg model with a high fidelity.