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Max-Cut graph-driven quantum circuit design for geometrically frustrated planar spin systems with spin-glass-like energy landscapes

Seyed Ehsan Ghasempouri*

Gerhard W. Dueck†

Stijn De Baerdemacker‡

  • *Contact author: ehsan.ghasempouri@unb.ca
  • †Contact author: gdueck@unb.ca
  • ‡Contact author: stijn.debaerdemacker@unb.ca
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Phys. Rev. Research 8, 043084 – Published 22 October, 2026

DOI: https://doi.org/10.1103/prhg-3t42

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 formalism, the current paradigm for noisy intermediate-scale quantum 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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Phys. Rev. Research 8, 043084– Published 22 October, 2026
  • Received 2 May 2025
  • Accepted 26 August 2026
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