Taming Complexity: Quantum Annealers Tackle Long-Range Interactions

Author: Denis Avetisyan

Researchers demonstrate the ability of quantum annealing to find ground states in complex classical systems, opening new avenues for simulating materials and quantum phenomena.

The optimization scheme transforms complex, long-range interactions into manageable unit-cell models, enabling the determination of optimal material states through either quantum annealing or classical algorithms, ultimately revealing the thermodynamic properties of the original system—a process reflecting the inherent tendency of complex systems to seek minimal energy configurations.

This review details the successful application of commercially available D-Wave quantum annealers to solve lattice models featuring competing long-range interactions, bridging the gap between quantum hardware and simulations in condensed matter physics and quantum optics.

Determining the ground state of complex, interacting spin systems remains a significant challenge in condensed matter physics and quantum simulation. This is addressed in ‘Quantum annealing for lattice models with competing long-range interactions’, which demonstrates a unit-cell-based optimization scheme utilizing commercial quantum annealing hardware to tackle classically-intractable Ising models with algebraically decaying long-range interactions. The approach successfully determines ground states on lattices relevant to quantum materials and quantum simulators, bridging a gap between current quantum technology and complex physical systems. Could this methodology pave the way for a more effective exploration of frustrated magnetism and emergent phenomena in materials science?

The Inevitable Complexity of Systems

Many physical systems are effectively modeled using complex Lattice Models, crucial for understanding material properties and interactions. These models simulate materials under diverse conditions, finding applications in condensed matter physics, materials science, and computational biology.

Finding the ground state – the lowest energy configuration – is computationally challenging, particularly with long-range interactions. Classical methods struggle due to exponentially scaling search spaces, often becoming trapped in local minima. This necessitates exploring alternative computational paradigms.

The anisotropic Shastry-Sutherland lattice of $Er_2Be_2GeO_7$ incorporates realistic Ising couplings and interatomic distances, influencing the magnetic configurations observed at magnetizations of 0, 1/4, and 1/2, as determined by quantum annealing optimization.

The Long-Range Ising Model, with its complex behavior, is notoriously difficult to solve. Unlike short-range interactions, long-range interactions create intricate correlations, frustrating the search for stability. This model serves as a valuable testbed for novel algorithms, a precarious phase in inevitable decline.

Seeking Lower States: A Quantum Approach

Optimization in complex systems often requires navigating rugged solution spaces. Traditional algorithms can become trapped in local minima, hindering the discovery of globally optimal solutions. Quantum Annealing offers a heuristic method for finding the minimum energy state of a given problem.

The D-Wave Advantage System employs superconducting qubits to explore the solution space more efficiently than classical counterparts. Leveraging quantum tunneling, the system increases the probability of finding the global minimum, and its performance is benchmarked against classical techniques.

Central to this approach is the Ising Problem formulation, mapping the optimization problem onto the quantum annealer. Representing the system’s energy as a function of spin variables, this mapping facilitates applying quantum annealing to a broad range of combinatorial optimization problems.

A devil’s staircase of ground-state magnetization plateaux emerges in the dipolar antiferromagnetic long-range interacting model on a triangular lattice, exhibiting consistent results between classical naive greedy optimization and quantum annealing on the D-Wave Advantage™ system.

Simplifying the Complex: A Unit-Cell Strategy

A novel approach optimizes complex lattice systems using a Unit-Cell-Based Optimization Scheme. This methodology simplifies the computational challenge by refining models applied to individual unit cells, rather than optimizing the entire lattice simultaneously, offering a significant reduction in complexity for systems with repeating motifs.

Quantum annealing optimization reveals a candidate ground state for the dipolar antiferromagnetic long-range interacting model on the Kagomé lattice, characterized by alternating spin orientations (represented by blue and red circles) within the unit cell.

This scheme’s versatility has been demonstrated with the Kagome and Shastry-Sutherland Lattices. Classical Binary Optimization techniques refine unit cell models prior to quantum annealing. Reliable optimal states were identified for unit cells containing up to 12 sites, though performance decreased with larger, 36-site cells, indicating scalability limits.

Mapping the Problem: From Lattice to Qubits

The Minor Embedding technique is critical for leveraging the D-Wave Advantage system. This process maps complex optimization problems onto the Pegasus Graph, defining the quantum annealer’s connectivity architecture. Without effective minor embedding, problems exceeding native qubit connectivity cannot be solved.

This capability is particularly important for All-to-All Connected Problems, which do not align with the restricted connectivity of the quantum processor. The Ocean SDK provides a toolkit for implementing minor embedding and programming the D-Wave system, translating optimization goals into a quantum-compatible form.

Recent experiments demonstrate comparable results to classical algorithms while significantly reducing computation time. A specific problem instance was solved in 10 minutes using the D-Wave system, compared to 2500 minutes (35 hours) of CPU time on a dual Intel Icelake 8360Y processor. Like all improvements, this acceleration ages faster than expected, a fleeting victory against inevitable entropy.

Toward Greater Resolution: Beyond Current Limits

The observed Devil’s Staircase in the Long-Range Ising Model provides a benchmark for assessing the accuracy and efficiency of the implemented quantum annealing scheme. This complex energy landscape, characterized by cascading phase transitions, highlights the potential advantages of quantum annealing for solving optimization problems.

This work paves the way for exploring more complex lattice models and investigating novel materials with tailored properties. By extending the methodology to higher dimensions and incorporating different interaction terms, researchers can simulate a wider range of physical phenomena, accelerating the discovery of materials with specific functionalities.

Future research will focus on refining the unit-cell optimization scheme and leveraging advanced quantum annealing algorithms to achieve greater computational advantages. Utilizing 1000 annealing runs served as a trade-off to determine optimal states for unit cells up to approximately 30 sites. Further improvements in algorithm efficiency and scalability will enable the study of even larger and more complex systems, pushing the boundaries of quantum simulation.

The pursuit of ground states, as detailed in this work concerning long-range Ising models, echoes a fundamental truth about complex systems. They invariably trend towards states of minimal energy, a process often obscured by the sheer scale of interaction. This mirrors the observation that systems learn to age gracefully, finding equilibrium not through forced optimization, but through the natural dissipation of energy. As Werner Heisenberg noted, “The very act of observing changes an object.” Similarly, attempting to force a solution onto a complex system—like finding the ground state—can disrupt the natural tendency towards equilibrium. Sometimes observing the process, allowing the system to evolve within the constraints of its interactions, yields a more insightful understanding than attempting to accelerate it towards a predetermined outcome.

The Horizon Recedes

The successful mapping of long-range interactions onto current quantum annealing hardware represents less a resolution than a sophisticated versioning of the problem. Each iteration of device architecture, each refinement in embedding techniques, allows for the accommodation of increasingly complex classical Hamiltonians. This is not progress toward an absolute ground state, but a graceful decay – a shifting of the boundary between what is tractable and what remains stubbornly beyond reach. The inherent limitations of connectivity, the persistent shadow of decoherence, these are not bugs to be fixed, but fundamental constraints defining the shape of the search space.

Future work will undoubtedly focus on scaling – attempting to push the system size toward the thermodynamic limit. However, the arrow of time always points toward refactoring. A more fruitful path may lie in exploring alternative mappings, leveraging the unique constraints of the hardware to illuminate specific, physically relevant instances of these long-range models. The true test will not be whether these machines can solve the most general case, but whether they can offer novel insights into systems where classical methods falter.

Ultimately, the value of this approach resides not in achieving a perfect solution, but in the iterative process of approximation. Each attempt to embed a classical system onto a quantum substrate reveals something new about both – a gentle erosion of the boundary between the classical and quantum realms, a reminder that even the most elegant theory is merely a temporary scaffolding against the inevitable advance of entropy.

Original article: https://arxiv.org/pdf/2511.08336.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/