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arXiv · 1909.08846

Almost optimal classical approximation algorithms for a quantum generalization of Max-Cut

Sevag Gharibian·Ojas Parekh
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Abstract

Approximation algorithms for constraint satisfaction problems (CSPs) are a central direction of study in theoretical computer science. In this work, we study classical product state approximation algorithms for a physically motivated quantum generalization of Max-Cut, known as the quantum Heisenberg model. This model is notoriously difficult to solve exactly, even on bipartite graphs, in stark contrast to the classical setting of Max-Cut. Here we show, for any interaction graph, how to classically and efficiently obtain approximation ratios 0.649 (anti-ferromagnetic XY model) and 0.498 (anti-ferromagnetic Heisenberg XYZ model). These are almost optimal; we show that the best possible ratios achievable by a product state for these models is 2/3 and 1/2, respectively.

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Sevag Gharibian, Ojas Parekh. 2019-09-19. Almost optimal classical approximation algorithms for a quantum generalization of Max-Cut. https://doi.org/10.4230/lipics.approx-random.2019.31

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