Approximation Algorithms for Quantum Max-$d$-Cut

• URL: http://arxiv.org/abs/2309.10957v2
• Date: Wed, 21 Feb 2024 04:29:01 GMT
• Title: Approximation Algorithms for Quantum Max-$d$-Cut
• Authors: Charlie Carlson, Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, Stuart Wayland
• Abstract summary: The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. We develop an algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees.
• Score: 42.248442410060946
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We initiate the algorithmic study of the Quantum Max-$d$-Cut problem, a quantum generalization of the well-known Max-$d$-Cut problem. The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. Equivalently, this problem is physically motivated by the $SU(d)$-Heisenberg model, a spin glass model that generalized the well-known Heisenberg model over qudits. We develop a polynomial-time randomized approximation algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees. Moreover, we prove the tightness of our analysis by presenting an algorithmic gap instance for Quantum Max-d-Cut problem with $d \geq 3$.

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