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arXiv · 2103.09090

Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing

Jiří Lebl·Asif Shakeel
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Abstract

Algorithmic discrepancy theory seeks efficient algorithms to find those two-colorings of a set that minimize a given measure of coloring imbalance in the set, its {\it discrepancy}. The {\it Euclidean discrepancy} problem and the problem of balancing covariates in randomized trials have efficient randomized algorithms based on the Gram-Schmidt walk (GSW). We frame these problems as quantum Ising models, for which variational quantum algorithms (VQA) are particularly useful. Simulating an example of covariate-balancing on an IBM quantum simulator, we find that the variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) yield results comparable to the GSW algorithm.

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Jiří Lebl, Asif Shakeel. 2021-03-16. Variational Quantum Algorithms for Euclidean Discrepancy and Covariate-Balancing. https://arxiv.org/abs/2103.09090

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