Max-Cut graph-driven quantum circuit design for planar spin glasses
Bibliographic record
Abstract
Finding the ground state of geometrically frustrated spin systems is a challenging problem with broad implications. Many hard optimization problems, including NP-complete problems, can be mapped, for instance, to frustrated Ising models, where competing interactions produce rugged, spin glass like energy landscapes. The difficulty is particularly pronounced in the weak-field regime, where geometrical frustration dominates, and the spectral gap becomes exponentially small, making it hard to identify the true ground state. In this work, we consider planar frustrated lattices constructed from the triangular motif, the minimal unit of geometrical frustration. We present a graph-based approach that allows for accurate state initialization of a frustrated triangular spin lattice with up to 20 sites while avoiding barren plateaus. To optimize circuit efficiency and trainability, we employ a clustering strategy that organizes qubits into distinct groups based on the maximum cut technique, which divides the lattice into two maximally disconnected subsets. We provide evidence that this Max Cut based lattice division offers a robust framework for optimizing circuit design and effectively modeling frustrated systems at polynomial cost. All simulations are performed within the variational quantum eigensolver (VQE) formalism, the current paradigm for noisy intermediate-scale quantum (NISQ) devices, but can be extended beyond. Our results underscore the potential of hybrid quantum classical methods in addressing complex optimization problems.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".