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Bulletin of the American Physical Society

Enhancing Combinatorial Optimization with Quantum Generative Models

Francisco Fernandez Alcazar, Alejandro Perdomo‐Ortiz

Published Mar 18, 2021• 0 citations
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Combinatorial optimization is one of the key candidates in the race for practical quantum advantage. In this work, we introduce a new family of quantum-enhanced optimizers and demonstrate how quantum machine learning models known as quantum generative models can find lower minima than those found by means of stand-alone state-of-the-art classical solvers. We present two new quantum-enhanced optimization strategies. The first scheme leverages data points evaluated during the optimization search from any quantum or classical optimizer. In this scheme, we show how our quantum generative model boosts the performance of classical solvers in hard-to-solve instances where the classical solver is not capable of making progress as a stand-alone strategy. The second quantum optimization strategy works as a stand-alone solver. Here we show its superior performance when the goal is to find the best minimum within the least number of cost function evaluations. Under this setting, we benchmark our quantum-enhanced optimization strategies against several solvers, including Bayesian optimizers which are known to be one of the best competing solvers in such tasks. To illustrate our findings, these benchmarks are performed in the context of the portfolio optimization problem by constructing instances from the S&P 500 stock market index. We show that our quantum-inspired generative models based on tensor networks generalize to unseen candidates with lower cost function values than any of the candidates seen by the classical solvers. This is the first demonstration of the generalization capabilities of quantum generative models that brings real value in the context of an industrial-scale application.
In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.