An improved Quantum Max Cut approximation via matching
Abstract
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to gain a provable and practical quantum advantage. A line of recent studies focuses on Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee [Lee, 2022] (0.562, generic input graph) and King [King, 2023] (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms.
Cite
@article{arxiv.2401.03616,
title = {An improved Quantum Max Cut approximation via matching},
author = {Eunou Lee and Ojas Parekh},
journal= {arXiv preprint arXiv:2401.03616},
year = {2026}
}