Quantum annealing for lattice models with competing long-range interactions

TL;DR

This paper demonstrates using superconducting qubit quantum annealing with a unit-cell optimization scheme to find ground states of long-range interacting Ising models, relevant for quantum simulation and material science.

Contribution

Introduces a unit-cell-based optimization method enabling quantum annealing of large lattice models with long-range interactions.

Findings

Successfully computed magnetization plateaux in long-range Ising models.

Determined ground states on Kagome lattice relevant for spin ice.

Analyzed models with additional interactions for frustrated Ising systems.

Abstract

We use superconducting qubit quantum annealing devices to determine the ground state of Ising models with algebraically decaying competing long-range interactions in the thermodynamic limit. This is enabled by a unit-cell-based optimization scheme, in which the finite optimizations on each unit cell are performed using commercial quantum annealing hardware. To demonstrate the capabilities of the approach, we choose three exemplary problems relevant for other quantum simulation platforms and material science: (i) the calculation of devil's staircases of magnetization plateaux of the long-range Ising model in a longitudinal field on the triangular lattice, motivated by atomic and molecular quantum simulators; (ii) the evaluation of the ground state of the same model on the Kagome lattice in the absence of a field, motivated by artificial spin ice metamaterials; (iii) the study of models with additional few-nearest-neighbor interactions relevant for frustrated Ising compounds with potential long-range interactions. The approach discussed in this work provides a useful and realistic application of existing quantum annealing technology, applicable across many research areas in which lattice problems with resummable long-range interactions are relevant.