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arXiv:2511.08336 · Communications Physics

Quantum annealing for lattice models with competing long-range interactions

Jan Alexander Koziol, Kai Phillip Schmidt

quant-phcond-mat.str-elphysics.comp-phSubmitted Nov 11, 2025• Announced Nov 12, 2025• 0 citations
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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.

Comments
8 pages, 4 figures

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Preparing 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 prepare 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 prepare ground states of the two-dimensional Heisenberg model with a high fidelity.
Abstract Quantum annealing provides a way of solving optimization problems by encoding them as Ising spin models which are implemented using physical qubits. The solution of the optimization problem then corresponds to the ground state of the system. Quantum tunneling is harnessed to enable the system to move to the ground state in a potentially high non-convex energy landscape. A major difficulty in encoding optimization problems in physical quantum annealing devices is the fact that many real world optimization problems require interactions of higher connectivity, as well as multi-body terms beyond the limitations of the physical hardware. In this work we address the question of how to implement multi-body interactions using hardware which natively only provides two-body interactions. The main result is an efficient circuit design of such multi-body terms using superconducting flux qubits in which effective N -body interactions are implemented using N ancilla qubits and only two inductive couplers. It is then shown how this circuit can be used as the unit cell of a scalable architecture by applying it to a recently proposed embedding technique for constructing an architecture of logical qubits with arbitrary connectivity using physical qubits which have nearest-neighbor four-body interactions. It is further shown that this design is robust to non-linear effects in the coupling loops, as well as mismatches in some of the circuit parameters.