Josep Bosch | Searcharxiv

arXiv2026

Reshaping quantum annealing landscapes with diagonal catalysts

Quantum annealing is often limited by population trapped in local minima many spin flips from the solution. We introduce a mathematical framework to understand the connection between energy and Hamming distance in optimization problems. Using this, we build ZZ-catalysts from ground-state patterns of small frustration-free subproblems that make configurations far from the solution less energetically competitive. On sparse problems they multiply the near-solution probability at short sweeps, with gains persisting on fully-connected models and tunable via subproblem choice.

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arXiv2024

A coherent approach to quantum-classical optimization

Hybrid quantum-classical optimization techniques, which incorporate the pre-optimization of Variational Quantum Algorithms (VQAs) using Tensor Networks (TNs), have been shown to allow for the reduction of quantum computational resources. In the particular case of large optimization problems, commonly found in real-world use cases, this strategy is almost mandatory to reduce the otherwise unfathomable execution costs and improve the quality of the results. We identify the coherence entropy as a crucial metric in determining the suitability of quantum states as effective initialization candidates. Our findings are validated through extensive numerical tests for the Quantum Approximate Optimization Algorithm (QAOA), in which we find that the optimal initialization states are pure Gibbs states. Further, these results are explained with the inclusion of a simple and yet novel notion of expressivity adapted to classical optimization problems. Based on this finding, we propose a quantum-classical optimization protocol that significantly improves on previous approaches for such tasks, with specific focus on its effectiveness.

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