Enhancing combinatorial optimization with classical and quantum generative models

Javier Alcazar, Mohammad Ghazi Vakili, Can B. Kalayci and Alejandro Perdomo-Ortiz ()
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Javier Alcazar: Zapata Computing Canada Inc.
Mohammad Ghazi Vakili: Zapata Computing Canada Inc.
Can B. Kalayci: Zapata Computing Canada Inc.
Alejandro Perdomo-Ortiz: Zapata Computing Canada Inc.

Nature Communications, 2024, vol. 15, issue 1, 1-9

Abstract: Abstract Devising an efficient exploration of the search space is one of the key challenges in the design of combinatorial optimization algorithms. Here, we introduce the Generator-Enhanced Optimization (GEO) strategy: a framework that leverages any generative model (classical, quantum, or quantum-inspired) to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. To illustrate our results, we run these benchmarks in the context of the canonical cardinality-constrained portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes, and demonstrate how the generalization capabilities of these quantum-inspired generative models can provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms and show that TN-GEO is among the best; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. Also, a promising step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models

Date: 2024
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DOI: 10.1038/s41467-024-46959-5

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